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Simplifying (x + -4)(3x + 3) = (x + 6)(x + -2) Reorder the terms: (-4 + x)(3x + 3) = (x + 6)(x + -2) Reorder the terms: (-4 + x)(3 + 3x) = (x + 6)(x + -2) Multiply (-4 + x) * (3 + 3x) (-4(3 + 3x) + x(3 + 3x)) = (x + 6)(x + -2) ((3 * -4 + 3x * -4) + x(3 + 3x)) = (x + 6)(x + -2) ((-12 + -12x) + x(3 + 3x)) = (x + 6)(x + -2) (-12 + -12x + (3 * x + 3x * x)) = (x + 6)(x + -2) (-12 + -12x + (3x + 3x2)) = (x + 6)(x + -2) Combine like terms: -12x + 3x = -9x (-12 + -9x + 3x2) = (x + 6)(x + -2) Reorder the terms: -12 + -9x + 3x2 = (6 + x)(x + -2) Reorder the terms: -12 + -9x + 3x2 = (6 + x)(-2 + x) Multiply (6 + x) * (-2 + x) -12 + -9x + 3x2 = (6(-2 + x) + x(-2 + x)) -12 + -9x + 3x2 = ((-2 * 6 + x * 6) + x(-2 + x)) -12 + -9x + 3x2 = ((-12 + 6x) + x(-2 + x)) -12 + -9x + 3x2 = (-12 + 6x + (-2 * x + x * x)) -12 + -9x + 3x2 = (-12 + 6x + (-2x + x2)) Combine like terms: 6x + -2x = 4x -12 + -9x + 3x2 = (-12 + 4x + x2) Add '12' to each side of the equation. -12 + -9x + 12 + 3x2 = -12 + 4x + 12 + x2 Reorder the terms: -12 + 12 + -9x + 3x2 = -12 + 4x + 12 + x2 Combine like terms: -12 + 12 = 0 0 + -9x + 3x2 = -12 + 4x + 12 + x2 -9x + 3x2 = -12 + 4x + 12 + x2 Reorder the terms: -9x + 3x2 = -12 + 12 + 4x + x2 Combine like terms: -12 + 12 = 0 -9x + 3x2 = 0 + 4x + x2 -9x + 3x2 = 4x + x2 Solving -9x + 3x2 = 4x + x2 Solving for variable 'x'. Reorder the terms: -9x + -4x + 3x2 + -1x2 = 4x + x2 + -4x + -1x2 Combine like terms: -9x + -4x = -13x -13x + 3x2 + -1x2 = 4x + x2 + -4x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -13x + 2x2 = 4x + x2 + -4x + -1x2 Reorder the terms: -13x + 2x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -13x + 2x2 = 0 + x2 + -1x2 -13x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -13x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-13 + 2x) = 0Subproblem 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 '(-13 + 2x)' equal to zero and attempt to solve: Simplifying -13 + 2x = 0 Solving -13 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2x = 0 + 13 2x = 0 + 13 Combine like terms: 0 + 13 = 13 2x = 13 Divide each side by '2'. x = 6.5 Simplifying x = 6.5Solution
x = {0, 6.5}
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