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Simplifying 3(2x + 1)(5x + -3) = 0 Reorder the terms: 3(1 + 2x)(5x + -3) = 0 Reorder the terms: 3(1 + 2x)(-3 + 5x) = 0 Multiply (1 + 2x) * (-3 + 5x) 3(1(-3 + 5x) + 2x * (-3 + 5x)) = 0 3((-3 * 1 + 5x * 1) + 2x * (-3 + 5x)) = 0 3((-3 + 5x) + 2x * (-3 + 5x)) = 0 3(-3 + 5x + (-3 * 2x + 5x * 2x)) = 0 3(-3 + 5x + (-6x + 10x2)) = 0 Combine like terms: 5x + -6x = -1x 3(-3 + -1x + 10x2) = 0 (-3 * 3 + -1x * 3 + 10x2 * 3) = 0 (-9 + -3x + 30x2) = 0 Solving -9 + -3x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -1x + 10x2) = 0 Factor a trinomial. 3((-1 + -2x)(3 + -5x)) = 0 Ignore the factor 3.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 '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {-0.5, 0.6}
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