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Simplifying (x + -5)(7x + 3) = -18(x + -5) Reorder the terms: (-5 + x)(7x + 3) = -18(x + -5) Reorder the terms: (-5 + x)(3 + 7x) = -18(x + -5) Multiply (-5 + x) * (3 + 7x) (-5(3 + 7x) + x(3 + 7x)) = -18(x + -5) ((3 * -5 + 7x * -5) + x(3 + 7x)) = -18(x + -5) ((-15 + -35x) + x(3 + 7x)) = -18(x + -5) (-15 + -35x + (3 * x + 7x * x)) = -18(x + -5) (-15 + -35x + (3x + 7x2)) = -18(x + -5) Combine like terms: -35x + 3x = -32x (-15 + -32x + 7x2) = -18(x + -5) Reorder the terms: -15 + -32x + 7x2 = -18(-5 + x) -15 + -32x + 7x2 = (-5 * -18 + x * -18) -15 + -32x + 7x2 = (90 + -18x) Solving -15 + -32x + 7x2 = 90 + -18x Solving for variable 'x'. Reorder the terms: -15 + -90 + -32x + 18x + 7x2 = 90 + -18x + -90 + 18x Combine like terms: -15 + -90 = -105 -105 + -32x + 18x + 7x2 = 90 + -18x + -90 + 18x Combine like terms: -32x + 18x = -14x -105 + -14x + 7x2 = 90 + -18x + -90 + 18x Reorder the terms: -105 + -14x + 7x2 = 90 + -90 + -18x + 18x Combine like terms: 90 + -90 = 0 -105 + -14x + 7x2 = 0 + -18x + 18x -105 + -14x + 7x2 = -18x + 18x Combine like terms: -18x + 18x = 0 -105 + -14x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-15 + -2x + x2) = 0 Factor a trinomial. 7((-3 + -1x)(5 + -1x)) = 0 Ignore the factor 7.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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-3, 5}
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