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Simplifying (12x + 5)(3x + 2) = 0 Reorder the terms: (5 + 12x)(3x + 2) = 0 Reorder the terms: (5 + 12x)(2 + 3x) = 0 Multiply (5 + 12x) * (2 + 3x) (5(2 + 3x) + 12x * (2 + 3x)) = 0 ((2 * 5 + 3x * 5) + 12x * (2 + 3x)) = 0 ((10 + 15x) + 12x * (2 + 3x)) = 0 (10 + 15x + (2 * 12x + 3x * 12x)) = 0 (10 + 15x + (24x + 36x2)) = 0 Combine like terms: 15x + 24x = 39x (10 + 39x + 36x2) = 0 Solving 10 + 39x + 36x2 = 0 Solving for variable 'x'. Factor a trinomial. (2 + 3x)(5 + 12x) = 0Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 2
Set the factor '(5 + 12x)' equal to zero and attempt to solve: Simplifying 5 + 12x = 0 Solving 5 + 12x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 12x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 12x = 0 + -5 12x = 0 + -5 Combine like terms: 0 + -5 = -5 12x = -5 Divide each side by '12'. x = -0.4166666667 Simplifying x = -0.4166666667Solution
x = {-0.6666666667, -0.4166666667}
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