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Simplifying 2x(x + -3) = 8 Reorder the terms: 2x(-3 + x) = 8 (-3 * 2x + x * 2x) = 8 (-6x + 2x^{2}) = 8 Solving -6x + 2x^{2}= 8 Solving for variable 'x'. Reorder the terms: -8 + -6x + 2x^{2}= 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -6x + 2x^{2}= 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -3x + x^{2}) = 0 Factor a trinomial. 2((-1 + -1x)(4 + -1x)) = 0 Ignore the factor 2.## Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1## Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4## Solution

x = {-1, 4}

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