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Simplifying (x + 42)(2x + 1) * x = 0 Reorder the terms: (42 + x)(2x + 1) * x = 0 Reorder the terms: (42 + x)(1 + 2x) * x = 0 Reorder the terms for easier multiplication: x(42 + x)(1 + 2x) = 0 Multiply (42 + x) * (1 + 2x) x(42(1 + 2x) + x(1 + 2x)) = 0 x((1 * 42 + 2x * 42) + x(1 + 2x)) = 0 x((42 + 84x) + x(1 + 2x)) = 0 x(42 + 84x + (1 * x + 2x * x)) = 0 x(42 + 84x + (1x + 2x2)) = 0 Combine like terms: 84x + 1x = 85x x(42 + 85x + 2x2) = 0 (42 * x + 85x * x + 2x2 * x) = 0 (42x + 85x2 + 2x3) = 0 Solving 42x + 85x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(42 + 85x + 2x2) = 0 Factor a trinomial. x((42 + x)(1 + 2x)) = 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 '(42 + x)' equal to zero and attempt to solve: Simplifying 42 + x = 0 Solving 42 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + x = 0 + -42 Combine like terms: 42 + -42 = 0 0 + x = 0 + -42 x = 0 + -42 Combine like terms: 0 + -42 = -42 x = -42 Simplifying x = -42Subproblem 3
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, -42, -0.5}
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