# 2x(x-3)=6

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## Solution for 2x(x-3)=6 equation:

Simplifying
2x(x + -3) = 6
Reorder the terms:
2x(-3 + x) = 6
(-3 * 2x + x * 2x) = 6
(-6x + 2x2) = 6
Solving
-6x + 2x2 = 6
Solving for variable 'x'.
Reorder the terms:
-6 + -6x + 2x2 = 6 + -6
Combine like terms: 6 + -6 = 0
-6 + -6x + 2x2 = 0
Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -3x + x2) = 0
Ignore the factor 2.
Subproblem 1Set the factor '(-3 + -3x + x2)' equal to zero and attempt to solve:
Simplifying
-3 + -3x + x2 = 0
Solving
-3 + -3x + x2 = 0
Begin completing the square.
Move the constant term to the right:
Add '3' to each side of the equation.
-3 + -3x + 3 + x2 = 0 + 3
Reorder the terms:
-3 + 3 + -3x + x2 = 0 + 3
Combine like terms: -3 + 3 = 0
0 + -3x + x2 = 0 + 3
-3x + x2 = 0 + 3
Combine like terms: 0 + 3 = 3
-3x + x2 = 3
The x term is -3x. Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.
Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 3 + 2.25
Reorder the terms:
2.25 + -3x + x2 = 3 + 2.25
Combine like terms: 3 + 2.25 = 5.25
2.25 + -3x + x2 = 5.25
Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 5.25
Calculate the square root of the right side: 2.291287847
Break this problem into two subproblems by setting
(x + -1.5) equal to 2.291287847 and -2.291287847.
Subproblem 1x + -1.5 = 2.291287847
Simplifying
x + -1.5 = 2.291287847
Reorder the terms:
-1.5 + x = 2.291287847
Solving
-1.5 + x = 2.291287847
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.291287847 + 1.5
Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.291287847 + 1.5
x = 2.291287847 + 1.5
Combine like terms: 2.291287847 + 1.5 = 3.791287847
x = 3.791287847
Simplifying
x = 3.791287847
Subproblem 2x + -1.5 = -2.291287847
Simplifying
x + -1.5 = -2.291287847
Reorder the terms:
-1.5 + x = -2.291287847
Solving
-1.5 + x = -2.291287847
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.291287847 + 1.5
Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.291287847 + 1.5
x = -2.291287847 + 1.5
Combine like terms: -2.291287847 + 1.5 = -0.791287847
x = -0.791287847
Simplifying
x = -0.791287847
SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {3.791287847, -0.791287847}Solutionx = {3.791287847, -0.791287847}`