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Simplifying (x + -3)(x + -2) = (x + 5)(2x + -3) + 21 Reorder the terms: (-3 + x)(x + -2) = (x + 5)(2x + -3) + 21 Reorder the terms: (-3 + x)(-2 + x) = (x + 5)(2x + -3) + 21 Multiply (-3 + x) * (-2 + x) (-3(-2 + x) + x(-2 + x)) = (x + 5)(2x + -3) + 21 ((-2 * -3 + x * -3) + x(-2 + x)) = (x + 5)(2x + -3) + 21 ((6 + -3x) + x(-2 + x)) = (x + 5)(2x + -3) + 21 (6 + -3x + (-2 * x + x * x)) = (x + 5)(2x + -3) + 21 (6 + -3x + (-2x + x2)) = (x + 5)(2x + -3) + 21 Combine like terms: -3x + -2x = -5x (6 + -5x + x2) = (x + 5)(2x + -3) + 21 Reorder the terms: 6 + -5x + x2 = (5 + x)(2x + -3) + 21 Reorder the terms: 6 + -5x + x2 = (5 + x)(-3 + 2x) + 21 Multiply (5 + x) * (-3 + 2x) 6 + -5x + x2 = (5(-3 + 2x) + x(-3 + 2x)) + 21 6 + -5x + x2 = ((-3 * 5 + 2x * 5) + x(-3 + 2x)) + 21 6 + -5x + x2 = ((-15 + 10x) + x(-3 + 2x)) + 21 6 + -5x + x2 = (-15 + 10x + (-3 * x + 2x * x)) + 21 6 + -5x + x2 = (-15 + 10x + (-3x + 2x2)) + 21 Combine like terms: 10x + -3x = 7x 6 + -5x + x2 = (-15 + 7x + 2x2) + 21 Reorder the terms: 6 + -5x + x2 = -15 + 21 + 7x + 2x2 Combine like terms: -15 + 21 = 6 6 + -5x + x2 = 6 + 7x + 2x2 Add '-6' to each side of the equation. 6 + -5x + -6 + x2 = 6 + 7x + -6 + 2x2 Reorder the terms: 6 + -6 + -5x + x2 = 6 + 7x + -6 + 2x2 Combine like terms: 6 + -6 = 0 0 + -5x + x2 = 6 + 7x + -6 + 2x2 -5x + x2 = 6 + 7x + -6 + 2x2 Reorder the terms: -5x + x2 = 6 + -6 + 7x + 2x2 Combine like terms: 6 + -6 = 0 -5x + x2 = 0 + 7x + 2x2 -5x + x2 = 7x + 2x2 Solving -5x + x2 = 7x + 2x2 Solving for variable 'x'. Reorder the terms: -5x + -7x + x2 + -2x2 = 7x + 2x2 + -7x + -2x2 Combine like terms: -5x + -7x = -12x -12x + x2 + -2x2 = 7x + 2x2 + -7x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -12x + -1x2 = 7x + 2x2 + -7x + -2x2 Reorder the terms: -12x + -1x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 -12x + -1x2 = 0 + 2x2 + -2x2 -12x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(12 + x) = 0 Ignore the factor -1.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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Solution
x = {0, -12}
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