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Simplifying (3x + 1)(2x + -2) = 64 Reorder the terms: (1 + 3x)(2x + -2) = 64 Reorder the terms: (1 + 3x)(-2 + 2x) = 64 Multiply (1 + 3x) * (-2 + 2x) (1(-2 + 2x) + 3x * (-2 + 2x)) = 64 ((-2 * 1 + 2x * 1) + 3x * (-2 + 2x)) = 64 ((-2 + 2x) + 3x * (-2 + 2x)) = 64 (-2 + 2x + (-2 * 3x + 2x * 3x)) = 64 (-2 + 2x + (-6x + 6x2)) = 64 Combine like terms: 2x + -6x = -4x (-2 + -4x + 6x2) = 64 Solving -2 + -4x + 6x2 = 64 Solving for variable 'x'. Reorder the terms: -2 + -64 + -4x + 6x2 = 64 + -64 Combine like terms: -2 + -64 = -66 -66 + -4x + 6x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -66 + -4x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + -2x + 3x2) = 0 Factor a trinomial. 2((-3 + -1x)(11 + -3x)) = 0 Ignore the factor 2.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 '(11 + -3x)' equal to zero and attempt to solve: Simplifying 11 + -3x = 0 Solving 11 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -3x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3x = 0 + -11 -3x = 0 + -11 Combine like terms: 0 + -11 = -11 -3x = -11 Divide each side by '-3'. x = 3.666666667 Simplifying x = 3.666666667Solution
x = {-3, 3.666666667}
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