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Simplifying (4x + -2)(5x + -6) = 0 Reorder the terms: (-2 + 4x)(5x + -6) = 0 Reorder the terms: (-2 + 4x)(-6 + 5x) = 0 Multiply (-2 + 4x) * (-6 + 5x) (-2(-6 + 5x) + 4x * (-6 + 5x)) = 0 ((-6 * -2 + 5x * -2) + 4x * (-6 + 5x)) = 0 ((12 + -10x) + 4x * (-6 + 5x)) = 0 (12 + -10x + (-6 * 4x + 5x * 4x)) = 0 (12 + -10x + (-24x + 20x2)) = 0 Combine like terms: -10x + -24x = -34x (12 + -34x + 20x2) = 0 Solving 12 + -34x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -17x + 10x2) = 0 Factor a trinomial. 2((1 + -2x)(6 + -5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2Solution
x = {0.5, 1.2}
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