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Simplifying x(x + 1)(6x + 5) = 0 Reorder the terms: x(1 + x)(6x + 5) = 0 Reorder the terms: x(1 + x)(5 + 6x) = 0 Multiply (1 + x) * (5 + 6x) x(1(5 + 6x) + x(5 + 6x)) = 0 x((5 * 1 + 6x * 1) + x(5 + 6x)) = 0 x((5 + 6x) + x(5 + 6x)) = 0 x(5 + 6x + (5 * x + 6x * x)) = 0 x(5 + 6x + (5x + 6x2)) = 0 Combine like terms: 6x + 5x = 11x x(5 + 11x + 6x2) = 0 (5 * x + 11x * x + 6x2 * x) = 0 (5x + 11x2 + 6x3) = 0 Solving 5x + 11x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 11x + 6x2) = 0 Factor a trinomial. x((1 + x)(5 + 6x)) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 3
Set the factor '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 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 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Divide each side by '6'. x = -0.8333333333 Simplifying x = -0.8333333333Solution
x = {0, -1, -0.8333333333}
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