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Simplifying (2 + 4x)(3 + 6x) = 0 Multiply (2 + 4x) * (3 + 6x) (2(3 + 6x) + 4x * (3 + 6x)) = 0 ((3 * 2 + 6x * 2) + 4x * (3 + 6x)) = 0 ((6 + 12x) + 4x * (3 + 6x)) = 0 (6 + 12x + (3 * 4x + 6x * 4x)) = 0 (6 + 12x + (12x + 24x2)) = 0 Combine like terms: 12x + 12x = 24x (6 + 24x + 24x2) = 0 Solving 6 + 24x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + 4x + 4x2) = 0 Factor a trinomial. 6((1 + 2x)(1 + 2x)) = 0 Ignore the factor 6.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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