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Simplifying 6(5x + -2)(2x + 3) = 0 Reorder the terms: 6(-2 + 5x)(2x + 3) = 0 Reorder the terms: 6(-2 + 5x)(3 + 2x) = 0 Multiply (-2 + 5x) * (3 + 2x) 6(-2(3 + 2x) + 5x * (3 + 2x)) = 0 6((3 * -2 + 2x * -2) + 5x * (3 + 2x)) = 0 6((-6 + -4x) + 5x * (3 + 2x)) = 0 6(-6 + -4x + (3 * 5x + 2x * 5x)) = 0 6(-6 + -4x + (15x + 10x2)) = 0 Combine like terms: -4x + 15x = 11x 6(-6 + 11x + 10x2) = 0 (-6 * 6 + 11x * 6 + 10x2 * 6) = 0 (-36 + 66x + 60x2) = 0 Solving -36 + 66x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-6 + 11x + 10x2) = 0 Factor a trinomial. 6((-3 + -2x)(2 + -5x)) = 0 Ignore the factor 6.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 '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 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 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4Solution
x = {-1.5, 0.4}
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