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Simplifying (8x + -9)(4x + 6) = 0 Reorder the terms: (-9 + 8x)(4x + 6) = 0 Reorder the terms: (-9 + 8x)(6 + 4x) = 0 Multiply (-9 + 8x) * (6 + 4x) (-9(6 + 4x) + 8x * (6 + 4x)) = 0 ((6 * -9 + 4x * -9) + 8x * (6 + 4x)) = 0 ((-54 + -36x) + 8x * (6 + 4x)) = 0 (-54 + -36x + (6 * 8x + 4x * 8x)) = 0 (-54 + -36x + (48x + 32x2)) = 0 Combine like terms: -36x + 48x = 12x (-54 + 12x + 32x2) = 0 Solving -54 + 12x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 6x + 16x2) = 0 Factor a trinomial. 2((-3 + -2x)(9 + -8x)) = 0 Ignore the factor 2.Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(9 + -8x)' equal to zero and attempt to solve: Simplifying 9 + -8x = 0 Solving 9 + -8x = 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 + -8x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8x = 0 + -9 -8x = 0 + -9 Combine like terms: 0 + -9 = -9 -8x = -9 Divide each side by '-8'. x = 1.125 Simplifying x = 1.125Solution
x = {-1.5, 1.125}
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