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Simplifying (3x + -2)(3x + -2) + (2x)(2x) = (3x + 2)(3x + 2) Reorder the terms: (-2 + 3x)(3x + -2) + (2x)(2x) = (3x + 2)(3x + 2) Reorder the terms: (-2 + 3x)(-2 + 3x) + (2x)(2x) = (3x + 2)(3x + 2) Multiply (-2 + 3x) * (-2 + 3x) (-2(-2 + 3x) + 3x * (-2 + 3x)) + (2x)(2x) = (3x + 2)(3x + 2) ((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) + (2x)(2x) = (3x + 2)(3x + 2) ((4 + -6x) + 3x * (-2 + 3x)) + (2x)(2x) = (3x + 2)(3x + 2) (4 + -6x + (-2 * 3x + 3x * 3x)) + (2x)(2x) = (3x + 2)(3x + 2) (4 + -6x + (-6x + 9x2)) + (2x)(2x) = (3x + 2)(3x + 2) Combine like terms: -6x + -6x = -12x (4 + -12x + 9x2) + (2x)(2x) = (3x + 2)(3x + 2) Remove parenthesis around (2x) 4 + -12x + 9x2 + 2x(2x) = (3x + 2)(3x + 2) Remove parenthesis around (2x) 4 + -12x + 9x2 + 2x * 2x = (3x + 2)(3x + 2) Reorder the terms for easier multiplication: 4 + -12x + 9x2 + 2 * 2x * x = (3x + 2)(3x + 2) Multiply 2 * 2 4 + -12x + 9x2 + 4x * x = (3x + 2)(3x + 2) Multiply x * x 4 + -12x + 9x2 + 4x2 = (3x + 2)(3x + 2) Combine like terms: 9x2 + 4x2 = 13x2 4 + -12x + 13x2 = (3x + 2)(3x + 2) Reorder the terms: 4 + -12x + 13x2 = (2 + 3x)(3x + 2) Reorder the terms: 4 + -12x + 13x2 = (2 + 3x)(2 + 3x) Multiply (2 + 3x) * (2 + 3x) 4 + -12x + 13x2 = (2(2 + 3x) + 3x * (2 + 3x)) 4 + -12x + 13x2 = ((2 * 2 + 3x * 2) + 3x * (2 + 3x)) 4 + -12x + 13x2 = ((4 + 6x) + 3x * (2 + 3x)) 4 + -12x + 13x2 = (4 + 6x + (2 * 3x + 3x * 3x)) 4 + -12x + 13x2 = (4 + 6x + (6x + 9x2)) Combine like terms: 6x + 6x = 12x 4 + -12x + 13x2 = (4 + 12x + 9x2) Add '-4' to each side of the equation. 4 + -12x + -4 + 13x2 = 4 + 12x + -4 + 9x2 Reorder the terms: 4 + -4 + -12x + 13x2 = 4 + 12x + -4 + 9x2 Combine like terms: 4 + -4 = 0 0 + -12x + 13x2 = 4 + 12x + -4 + 9x2 -12x + 13x2 = 4 + 12x + -4 + 9x2 Reorder the terms: -12x + 13x2 = 4 + -4 + 12x + 9x2 Combine like terms: 4 + -4 = 0 -12x + 13x2 = 0 + 12x + 9x2 -12x + 13x2 = 12x + 9x2 Solving -12x + 13x2 = 12x + 9x2 Solving for variable 'x'. Reorder the terms: -12x + -12x + 13x2 + -9x2 = 12x + 9x2 + -12x + -9x2 Combine like terms: -12x + -12x = -24x -24x + 13x2 + -9x2 = 12x + 9x2 + -12x + -9x2 Combine like terms: 13x2 + -9x2 = 4x2 -24x + 4x2 = 12x + 9x2 + -12x + -9x2 Reorder the terms: -24x + 4x2 = 12x + -12x + 9x2 + -9x2 Combine like terms: 12x + -12x = 0 -24x + 4x2 = 0 + 9x2 + -9x2 -24x + 4x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-6 + x) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Solution
x = {0, 6}
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