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Simplifying (x + -9)(4x + 3) = -9(x + -9) Reorder the terms: (-9 + x)(4x + 3) = -9(x + -9) Reorder the terms: (-9 + x)(3 + 4x) = -9(x + -9) Multiply (-9 + x) * (3 + 4x) (-9(3 + 4x) + x(3 + 4x)) = -9(x + -9) ((3 * -9 + 4x * -9) + x(3 + 4x)) = -9(x + -9) ((-27 + -36x) + x(3 + 4x)) = -9(x + -9) (-27 + -36x + (3 * x + 4x * x)) = -9(x + -9) (-27 + -36x + (3x + 4x2)) = -9(x + -9) Combine like terms: -36x + 3x = -33x (-27 + -33x + 4x2) = -9(x + -9) Reorder the terms: -27 + -33x + 4x2 = -9(-9 + x) -27 + -33x + 4x2 = (-9 * -9 + x * -9) -27 + -33x + 4x2 = (81 + -9x) Solving -27 + -33x + 4x2 = 81 + -9x Solving for variable 'x'. Reorder the terms: -27 + -81 + -33x + 9x + 4x2 = 81 + -9x + -81 + 9x Combine like terms: -27 + -81 = -108 -108 + -33x + 9x + 4x2 = 81 + -9x + -81 + 9x Combine like terms: -33x + 9x = -24x -108 + -24x + 4x2 = 81 + -9x + -81 + 9x Reorder the terms: -108 + -24x + 4x2 = 81 + -81 + -9x + 9x Combine like terms: 81 + -81 = 0 -108 + -24x + 4x2 = 0 + -9x + 9x -108 + -24x + 4x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -108 + -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + -6x + x2) = 0 Factor a trinomial. 4((-3 + -1x)(9 + -1x)) = 0 Ignore the factor 4.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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-3, 9}
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