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Simplifying (15x + 4)(12x + 6) = 0 Reorder the terms: (4 + 15x)(12x + 6) = 0 Reorder the terms: (4 + 15x)(6 + 12x) = 0 Multiply (4 + 15x) * (6 + 12x) (4(6 + 12x) + 15x * (6 + 12x)) = 0 ((6 * 4 + 12x * 4) + 15x * (6 + 12x)) = 0 ((24 + 48x) + 15x * (6 + 12x)) = 0 (24 + 48x + (6 * 15x + 12x * 15x)) = 0 (24 + 48x + (90x + 180x2)) = 0 Combine like terms: 48x + 90x = 138x (24 + 138x + 180x2) = 0 Solving 24 + 138x + 180x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + 23x + 30x2) = 0 Factor a trinomial. 6((1 + 2x)(4 + 15x)) = 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 '(4 + 15x)' equal to zero and attempt to solve: Simplifying 4 + 15x = 0 Solving 4 + 15x = 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 + 15x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 15x = 0 + -4 15x = 0 + -4 Combine like terms: 0 + -4 = -4 15x = -4 Divide each side by '15'. x = -0.2666666667 Simplifying x = -0.2666666667Solution
x = {-0.5, -0.2666666667}
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