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Simplifying 8x2 + -1x3 + x = x2 + 13x Reorder the terms: x + 8x2 + -1x3 = x2 + 13x Reorder the terms: x + 8x2 + -1x3 = 13x + x2 Solving x + 8x2 + -1x3 = 13x + x2 Solving for variable 'x'. Reorder the terms: x + -13x + 8x2 + -1x2 + -1x3 = 13x + x2 + -13x + -1x2 Combine like terms: x + -13x = -12x -12x + 8x2 + -1x2 + -1x3 = 13x + x2 + -13x + -1x2 Combine like terms: 8x2 + -1x2 = 7x2 -12x + 7x2 + -1x3 = 13x + x2 + -13x + -1x2 Reorder the terms: -12x + 7x2 + -1x3 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 -12x + 7x2 + -1x3 = 0 + x2 + -1x2 -12x + 7x2 + -1x3 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12x + 7x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + 7x + -1x2) = 0 Factor a trinomial. x((-4 + x)(3 + -1x)) = 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, 4, 3}
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