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Simplifying (4x + 6)(5x + -6) = 0 Reorder the terms: (6 + 4x)(5x + -6) = 0 Reorder the terms: (6 + 4x)(-6 + 5x) = 0 Multiply (6 + 4x) * (-6 + 5x) (6(-6 + 5x) + 4x * (-6 + 5x)) = 0 ((-6 * 6 + 5x * 6) + 4x * (-6 + 5x)) = 0 ((-36 + 30x) + 4x * (-6 + 5x)) = 0 (-36 + 30x + (-6 * 4x + 5x * 4x)) = 0 (-36 + 30x + (-24x + 20x2)) = 0 Combine like terms: 30x + -24x = 6x (-36 + 6x + 20x2) = 0 Solving -36 + 6x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 3x + 10x2) = 0 Factor a trinomial. 2((-3 + -2x)(6 + -5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, 1.2}
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