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Simplifying (-10x + 2)(2x + 3) = 0 Reorder the terms: (2 + -10x)(2x + 3) = 0 Reorder the terms: (2 + -10x)(3 + 2x) = 0 Multiply (2 + -10x) * (3 + 2x) (2(3 + 2x) + -10x * (3 + 2x)) = 0 ((3 * 2 + 2x * 2) + -10x * (3 + 2x)) = 0 ((6 + 4x) + -10x * (3 + 2x)) = 0 (6 + 4x + (3 * -10x + 2x * -10x)) = 0 (6 + 4x + (-30x + -20x2)) = 0 Combine like terms: 4x + -30x = -26x (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((1 + -5x)(3 + 2x)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.2Subproblem 2
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 = -1.5Solution
x = {0.2, -1.5}
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