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Simplifying (3x + -4y)(3x + -4y) = 0 Multiply (3x + -4y) * (3x + -4y) (3x * (3x + -4y) + -4y * (3x + -4y)) = 0 ((3x * 3x + -4y * 3x) + -4y * (3x + -4y)) = 0 Reorder the terms: ((-12xy + 9x^{2}) + -4y * (3x + -4y)) = 0 ((-12xy + 9x^{2}) + -4y * (3x + -4y)) = 0 (-12xy + 9x^{2}+ (3x * -4y + -4y * -4y)) = 0 (-12xy + 9x^{2}+ (-12xy + 16y^{2})) = 0 Reorder the terms: (-12xy + -12xy + 9x^{2}+ 16y^{2}) = 0 Combine like terms: -12xy + -12xy = -24xy (-24xy + 9x^{2}+ 16y^{2}) = 0 Solving -24xy + 9x^{2}+ 16y^{2}= 0 Solving for variable 'x'. Factor a trinomial. (3x + -4y)(3x + -4y) = 0## Subproblem 1

Set the factor '(3x + -4y)' equal to zero and attempt to solve: Simplifying 3x + -4y = 0 Solving 3x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 3x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 3x + 0 = 0 + 4y 3x = 0 + 4y Remove the zero: 3x = 4y Divide each side by '3'. x = 1.333333333y Simplifying x = 1.333333333y## Subproblem 2

Set the factor '(3x + -4y)' equal to zero and attempt to solve: Simplifying 3x + -4y = 0 Solving 3x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 3x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 3x + 0 = 0 + 4y 3x = 0 + 4y Remove the zero: 3x = 4y Divide each side by '3'. x = 1.333333333y Simplifying x = 1.333333333y## Solution

x = {1.333333333y, 1.333333333y}

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