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Simplifying (3x + -6)(2x + -1) = 0 Reorder the terms: (-6 + 3x)(2x + -1) = 0 Reorder the terms: (-6 + 3x)(-1 + 2x) = 0 Multiply (-6 + 3x) * (-1 + 2x) (-6(-1 + 2x) + 3x * (-1 + 2x)) = 0 ((-1 * -6 + 2x * -6) + 3x * (-1 + 2x)) = 0 ((6 + -12x) + 3x * (-1 + 2x)) = 0 (6 + -12x + (-1 * 3x + 2x * 3x)) = 0 (6 + -12x + (-3x + 6x2)) = 0 Combine like terms: -12x + -3x = -15x (6 + -15x + 6x2) = 0 Solving 6 + -15x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -5x + 2x2) = 0 Factor a trinomial. 3((1 + -2x)(2 + -1x)) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0.5, 2}
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