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Simplifying 12(5x + -1) = 7x(2x + 2) Reorder the terms: 12(-1 + 5x) = 7x(2x + 2) (-1 * 12 + 5x * 12) = 7x(2x + 2) (-12 + 60x) = 7x(2x + 2) Reorder the terms: -12 + 60x = 7x(2 + 2x) -12 + 60x = (2 * 7x + 2x * 7x) -12 + 60x = (14x + 14x2) Solving -12 + 60x = 14x + 14x2 Solving for variable 'x'. Combine like terms: 60x + -14x = 46x -12 + 46x + -14x2 = 14x + 14x2 + -14x + -14x2 Reorder the terms: -12 + 46x + -14x2 = 14x + -14x + 14x2 + -14x2 Combine like terms: 14x + -14x = 0 -12 + 46x + -14x2 = 0 + 14x2 + -14x2 -12 + 46x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -12 + 46x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 23x + -7x2) = 0 Factor a trinomial. 2((-3 + x)(2 + -7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 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 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857Solution
x = {3, 0.2857142857}
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