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Simplifying (14x + 7)(8x + -12) = 0 Reorder the terms: (7 + 14x)(8x + -12) = 0 Reorder the terms: (7 + 14x)(-12 + 8x) = 0 Multiply (7 + 14x) * (-12 + 8x) (7(-12 + 8x) + 14x * (-12 + 8x)) = 0 ((-12 * 7 + 8x * 7) + 14x * (-12 + 8x)) = 0 ((-84 + 56x) + 14x * (-12 + 8x)) = 0 (-84 + 56x + (-12 * 14x + 8x * 14x)) = 0 (-84 + 56x + (-168x + 112x2)) = 0 Combine like terms: 56x + -168x = -112x (-84 + -112x + 112x2) = 0 Solving -84 + -112x + 112x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '28'. 28(-3 + -4x + 4x2) = 0 Factor a trinomial. 28((-1 + -2x)(3 + -2x)) = 0 Ignore the factor 28.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-0.5, 1.5}
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