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Simplifying (2x + 1)(x + -4) = 9(x + -4) Reorder the terms: (1 + 2x)(x + -4) = 9(x + -4) Reorder the terms: (1 + 2x)(-4 + x) = 9(x + -4) Multiply (1 + 2x) * (-4 + x) (1(-4 + x) + 2x * (-4 + x)) = 9(x + -4) ((-4 * 1 + x * 1) + 2x * (-4 + x)) = 9(x + -4) ((-4 + 1x) + 2x * (-4 + x)) = 9(x + -4) (-4 + 1x + (-4 * 2x + x * 2x)) = 9(x + -4) (-4 + 1x + (-8x + 2x2)) = 9(x + -4) Combine like terms: 1x + -8x = -7x (-4 + -7x + 2x2) = 9(x + -4) Reorder the terms: -4 + -7x + 2x2 = 9(-4 + x) -4 + -7x + 2x2 = (-4 * 9 + x * 9) -4 + -7x + 2x2 = (-36 + 9x) Solving -4 + -7x + 2x2 = -36 + 9x Solving for variable 'x'. Reorder the terms: -4 + 36 + -7x + -9x + 2x2 = -36 + 9x + 36 + -9x Combine like terms: -4 + 36 = 32 32 + -7x + -9x + 2x2 = -36 + 9x + 36 + -9x Combine like terms: -7x + -9x = -16x 32 + -16x + 2x2 = -36 + 9x + 36 + -9x Reorder the terms: 32 + -16x + 2x2 = -36 + 36 + 9x + -9x Combine like terms: -36 + 36 = 0 32 + -16x + 2x2 = 0 + 9x + -9x 32 + -16x + 2x2 = 9x + -9x Combine like terms: 9x + -9x = 0 32 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -8x + x2) = 0 Factor a trinomial. 2((4 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = 4Subproblem 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 = {4, 4}
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