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Simplifying 9x(x + -4) = (2x + 7)(x + -4) Reorder the terms: 9x(-4 + x) = (2x + 7)(x + -4) (-4 * 9x + x * 9x) = (2x + 7)(x + -4) (-36x + 9x2) = (2x + 7)(x + -4) Reorder the terms: -36x + 9x2 = (7 + 2x)(x + -4) Reorder the terms: -36x + 9x2 = (7 + 2x)(-4 + x) Multiply (7 + 2x) * (-4 + x) -36x + 9x2 = (7(-4 + x) + 2x * (-4 + x)) -36x + 9x2 = ((-4 * 7 + x * 7) + 2x * (-4 + x)) -36x + 9x2 = ((-28 + 7x) + 2x * (-4 + x)) -36x + 9x2 = (-28 + 7x + (-4 * 2x + x * 2x)) -36x + 9x2 = (-28 + 7x + (-8x + 2x2)) Combine like terms: 7x + -8x = -1x -36x + 9x2 = (-28 + -1x + 2x2) Solving -36x + 9x2 = -28 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: 28 + -36x + x + 9x2 + -2x2 = -28 + -1x + 2x2 + 28 + x + -2x2 Combine like terms: -36x + x = -35x 28 + -35x + 9x2 + -2x2 = -28 + -1x + 2x2 + 28 + x + -2x2 Combine like terms: 9x2 + -2x2 = 7x2 28 + -35x + 7x2 = -28 + -1x + 2x2 + 28 + x + -2x2 Reorder the terms: 28 + -35x + 7x2 = -28 + 28 + -1x + x + 2x2 + -2x2 Combine like terms: -28 + 28 = 0 28 + -35x + 7x2 = 0 + -1x + x + 2x2 + -2x2 28 + -35x + 7x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 28 + -35x + 7x2 = 0 + 2x2 + -2x2 28 + -35x + 7x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 28 + -35x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(4 + -5x + x2) = 0 Factor a trinomial. 7((1 + -1x)(4 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {1, 4}
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