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Simplifying (x + -3)(x + -4) * 8 = 0 Reorder the terms: (-3 + x)(x + -4) * 8 = 0 Reorder the terms: (-3 + x)(-4 + x) * 8 = 0 Reorder the terms for easier multiplication: 8(-3 + x)(-4 + x) = 0 Multiply (-3 + x) * (-4 + x) 8(-3(-4 + x) + x(-4 + x)) = 0 8((-4 * -3 + x * -3) + x(-4 + x)) = 0 8((12 + -3x) + x(-4 + x)) = 0 8(12 + -3x + (-4 * x + x * x)) = 0 8(12 + -3x + (-4x + x2)) = 0 Combine like terms: -3x + -4x = -7x 8(12 + -7x + x2) = 0 (12 * 8 + -7x * 8 + x2 * 8) = 0 (96 + -56x + 8x2) = 0 Solving 96 + -56x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(12 + -7x + x2) = 0 Factor a trinomial. 8((3 + -1x)(4 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 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 = 4Solution
x = {3, 4}
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