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Simplifying (8x + 4)(6x + -9) = 0 Reorder the terms: (4 + 8x)(6x + -9) = 0 Reorder the terms: (4 + 8x)(-9 + 6x) = 0 Multiply (4 + 8x) * (-9 + 6x) (4(-9 + 6x) + 8x * (-9 + 6x)) = 0 ((-9 * 4 + 6x * 4) + 8x * (-9 + 6x)) = 0 ((-36 + 24x) + 8x * (-9 + 6x)) = 0 (-36 + 24x + (-9 * 8x + 6x * 8x)) = 0 (-36 + 24x + (-72x + 48x2)) = 0 Combine like terms: 24x + -72x = -48x (-36 + -48x + 48x2) = 0 Solving -36 + -48x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-3 + -4x + 4x2) = 0 Factor a trinomial. 12((-1 + -2x)(3 + -2x)) = 0 Ignore the factor 12.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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