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Simplifying 3(4 + -1x)(3 + 6x) = 0 Multiply (4 + -1x) * (3 + 6x) 3(4(3 + 6x) + -1x * (3 + 6x)) = 0 3((3 * 4 + 6x * 4) + -1x * (3 + 6x)) = 0 3((12 + 24x) + -1x * (3 + 6x)) = 0 3(12 + 24x + (3 * -1x + 6x * -1x)) = 0 3(12 + 24x + (-3x + -6x2)) = 0 Combine like terms: 24x + -3x = 21x 3(12 + 21x + -6x2) = 0 (12 * 3 + 21x * 3 + -6x2 * 3) = 0 (36 + 63x + -18x2) = 0 Solving 36 + 63x + -18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(4 + 7x + -2x2) = 0 Factor a trinomial. 9((4 + -1x)(1 + 2x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 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 = {4, -0.5}
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