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Simplifying (4x + 8)(2x + -9) = 0 Reorder the terms: (8 + 4x)(2x + -9) = 0 Reorder the terms: (8 + 4x)(-9 + 2x) = 0 Multiply (8 + 4x) * (-9 + 2x) (8(-9 + 2x) + 4x * (-9 + 2x)) = 0 ((-9 * 8 + 2x * 8) + 4x * (-9 + 2x)) = 0 ((-72 + 16x) + 4x * (-9 + 2x)) = 0 (-72 + 16x + (-9 * 4x + 2x * 4x)) = 0 (-72 + 16x + (-36x + 8x2)) = 0 Combine like terms: 16x + -36x = -20x (-72 + -20x + 8x2) = 0 Solving -72 + -20x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-18 + -5x + 2x2) = 0 Factor a trinomial. 4((-2 + -1x)(9 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {-2, 4.5}
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