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Simplifying ((6x + 7) * x(12x + 5)) = 0 Reorder the terms: ((7 + 6x) * x(12x + 5)) = 0 Reorder the terms: ((7 + 6x) * x(5 + 12x)) = 0 Reorder the terms for easier multiplication: (x(7 + 6x)(5 + 12x)) = 0 Multiply (7 + 6x) * (5 + 12x) (x(7(5 + 12x) + 6x * (5 + 12x))) = 0 (x((5 * 7 + 12x * 7) + 6x * (5 + 12x))) = 0 (x((35 + 84x) + 6x * (5 + 12x))) = 0 (x(35 + 84x + (5 * 6x + 12x * 6x))) = 0 (x(35 + 84x + (30x + 72x2))) = 0 Combine like terms: 84x + 30x = 114x (x(35 + 114x + 72x2)) = 0 ((35 * x + 114x * x + 72x2 * x)) = 0 ((35x + 114x2 + 72x3)) = 0 (35x + 114x2 + 72x3) = 0 Remove parenthesis around (35x + 114x2 + 72x3) 35x + 114x2 + 72x3 = 0 Solving 35x + 114x2 + 72x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(35 + 114x + 72x2) = 0 Factor a trinomial. x((7 + 6x)(5 + 12x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Divide each side by '6'. x = -1.166666667 Simplifying x = -1.166666667Subproblem 3
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, -1.166666667, -0.4166666667}
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