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Simplifying (3x + -31)(x + 59) * x = 0 Reorder the terms: (-31 + 3x)(x + 59) * x = 0 Reorder the terms: (-31 + 3x)(59 + x) * x = 0 Reorder the terms for easier multiplication: x(-31 + 3x)(59 + x) = 0 Multiply (-31 + 3x) * (59 + x) x(-31(59 + x) + 3x * (59 + x)) = 0 x((59 * -31 + x * -31) + 3x * (59 + x)) = 0 x((-1829 + -31x) + 3x * (59 + x)) = 0 x(-1829 + -31x + (59 * 3x + x * 3x)) = 0 x(-1829 + -31x + (177x + 3x2)) = 0 Combine like terms: -31x + 177x = 146x x(-1829 + 146x + 3x2) = 0 (-1829 * x + 146x * x + 3x2 * x) = 0 (-1829x + 146x2 + 3x3) = 0 Solving -1829x + 146x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1829 + 146x + 3x2) = 0 Factor a trinomial. x((-59 + -1x)(31 + -3x)) = 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 '(-59 + -1x)' equal to zero and attempt to solve: Simplifying -59 + -1x = 0 Solving -59 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '59' to each side of the equation. -59 + 59 + -1x = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -1x = 0 + 59 -1x = 0 + 59 Combine like terms: 0 + 59 = 59 -1x = 59 Divide each side by '-1'. x = -59 Simplifying x = -59Subproblem 3
Set the factor '(31 + -3x)' equal to zero and attempt to solve: Simplifying 31 + -3x = 0 Solving 31 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -3x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -3x = 0 + -31 -3x = 0 + -31 Combine like terms: 0 + -31 = -31 -3x = -31 Divide each side by '-3'. x = 10.33333333 Simplifying x = 10.33333333Solution
x = {0, -59, 10.33333333}
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