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Simplifying 7 + -7x = [(4x + 9)(x + -1)] Reorder the terms: 7 + -7x = [(9 + 4x)(x + -1)] Reorder the terms: 7 + -7x = [(9 + 4x)(-1 + x)] Multiply (9 + 4x) * (-1 + x) 7 + -7x = [(9(-1 + x) + 4x * (-1 + x))] 7 + -7x = [((-1 * 9 + x * 9) + 4x * (-1 + x))] 7 + -7x = [((-9 + 9x) + 4x * (-1 + x))] 7 + -7x = [(-9 + 9x + (-1 * 4x + x * 4x))] 7 + -7x = [(-9 + 9x + (-4x + 4x2))] Combine like terms: 9x + -4x = 5x 7 + -7x = [(-9 + 5x + 4x2)] 7 + -7x = [-9 + 5x + 4x2] Remove brackets around [-9 + 5x + 4x2] 7 + -7x = -9 + 5x + 4x2 Solving 7 + -7x = -9 + 5x + 4x2 Solving for variable 'x'. Reorder the terms: 7 + 9 + -7x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2 Combine like terms: 7 + 9 = 16 16 + -7x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2 Combine like terms: -7x + -5x = -12x 16 + -12x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2 Reorder the terms: 16 + -12x + -4x2 = -9 + 9 + 5x + -5x + 4x2 + -4x2 Combine like terms: -9 + 9 = 0 16 + -12x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2 16 + -12x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 16 + -12x + -4x2 = 0 + 4x2 + -4x2 16 + -12x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 16 + -12x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -3x + -1x2) = 0 Factor a trinomial. 4((1 + -1x)(4 + x)) = 0 Ignore the factor 4.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 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {1, -4}
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