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Simplifying (2x + 7)(5x + -9) = 2x + 7 Reorder the terms: (7 + 2x)(5x + -9) = 2x + 7 Reorder the terms: (7 + 2x)(-9 + 5x) = 2x + 7 Multiply (7 + 2x) * (-9 + 5x) (7(-9 + 5x) + 2x * (-9 + 5x)) = 2x + 7 ((-9 * 7 + 5x * 7) + 2x * (-9 + 5x)) = 2x + 7 ((-63 + 35x) + 2x * (-9 + 5x)) = 2x + 7 (-63 + 35x + (-9 * 2x + 5x * 2x)) = 2x + 7 (-63 + 35x + (-18x + 10x2)) = 2x + 7 Combine like terms: 35x + -18x = 17x (-63 + 17x + 10x2) = 2x + 7 Reorder the terms: -63 + 17x + 10x2 = 7 + 2x Solving -63 + 17x + 10x2 = 7 + 2x Solving for variable 'x'. Reorder the terms: -63 + -7 + 17x + -2x + 10x2 = 7 + 2x + -7 + -2x Combine like terms: -63 + -7 = -70 -70 + 17x + -2x + 10x2 = 7 + 2x + -7 + -2x Combine like terms: 17x + -2x = 15x -70 + 15x + 10x2 = 7 + 2x + -7 + -2x Reorder the terms: -70 + 15x + 10x2 = 7 + -7 + 2x + -2x Combine like terms: 7 + -7 = 0 -70 + 15x + 10x2 = 0 + 2x + -2x -70 + 15x + 10x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -70 + 15x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-14 + 3x + 2x2) = 0 Factor a trinomial. 5((-7 + -2x)(2 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-3.5, 2}
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