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Simplifying 3(4x + -3)(5x + 6) = 0 Reorder the terms: 3(-3 + 4x)(5x + 6) = 0 Reorder the terms: 3(-3 + 4x)(6 + 5x) = 0 Multiply (-3 + 4x) * (6 + 5x) 3(-3(6 + 5x) + 4x * (6 + 5x)) = 0 3((6 * -3 + 5x * -3) + 4x * (6 + 5x)) = 0 3((-18 + -15x) + 4x * (6 + 5x)) = 0 3(-18 + -15x + (6 * 4x + 5x * 4x)) = 0 3(-18 + -15x + (24x + 20x2)) = 0 Combine like terms: -15x + 24x = 9x 3(-18 + 9x + 20x2) = 0 (-18 * 3 + 9x * 3 + 20x2 * 3) = 0 (-54 + 27x + 60x2) = 0 Solving -54 + 27x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + 9x + 20x2) = 0 Factor a trinomial. 3((-6 + -5x)(3 + -4x)) = 0 Ignore the factor 3.Subproblem 1
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 = -1.2Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {-1.2, 0.75}
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