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Simplifying 3(4x + -2) * 2(6x + -3) = 0 Reorder the terms: 3(-2 + 4x) * 2(6x + -3) = 0 Reorder the terms: 3(-2 + 4x) * 2(-3 + 6x) = 0 Reorder the terms for easier multiplication: 3 * 2(-2 + 4x)(-3 + 6x) = 0 Multiply 3 * 2 6(-2 + 4x)(-3 + 6x) = 0 Multiply (-2 + 4x) * (-3 + 6x) 6(-2(-3 + 6x) + 4x * (-3 + 6x)) = 0 6((-3 * -2 + 6x * -2) + 4x * (-3 + 6x)) = 0 6((6 + -12x) + 4x * (-3 + 6x)) = 0 6(6 + -12x + (-3 * 4x + 6x * 4x)) = 0 6(6 + -12x + (-12x + 24x2)) = 0 Combine like terms: -12x + -12x = -24x 6(6 + -24x + 24x2) = 0 (6 * 6 + -24x * 6 + 24x2 * 6) = 0 (36 + -144x + 144x2) = 0 Solving 36 + -144x + 144x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '36'. 36(1 + -4x + 4x2) = 0 Factor a trinomial. 36((1 + -2x)(1 + -2x)) = 0 Ignore the factor 36.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 '(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 = 0.5Solution
x = {0.5, 0.5}
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