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Simplifying 2(3 + -2x)(1 + 5x) = 0 Multiply (3 + -2x) * (1 + 5x) 2(3(1 + 5x) + -2x * (1 + 5x)) = 0 2((1 * 3 + 5x * 3) + -2x * (1 + 5x)) = 0 2((3 + 15x) + -2x * (1 + 5x)) = 0 2(3 + 15x + (1 * -2x + 5x * -2x)) = 0 2(3 + 15x + (-2x + -10x2)) = 0 Combine like terms: 15x + -2x = 13x 2(3 + 13x + -10x2) = 0 (3 * 2 + 13x * 2 + -10x2 * 2) = 0 (6 + 26x + -20x2) = 0 Solving 6 + 26x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 13x + -10x2) = 0 Factor a trinomial. 2((3 + -2x)(1 + 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 '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Solution
x = {1.5, -0.2}
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