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Simplifying 2x5 + -10x3 + 12x = -15x + 11x3 Reorder the terms: 12x + -10x3 + 2x5 = -15x + 11x3 Solving 12x + -10x3 + 2x5 = -15x + 11x3 Solving for variable 'x'. Reorder the terms: 12x + 15x + -10x3 + -11x3 + 2x5 = -15x + 11x3 + 15x + -11x3 Combine like terms: 12x + 15x = 27x 27x + -10x3 + -11x3 + 2x5 = -15x + 11x3 + 15x + -11x3 Combine like terms: -10x3 + -11x3 = -21x3 27x + -21x3 + 2x5 = -15x + 11x3 + 15x + -11x3 Reorder the terms: 27x + -21x3 + 2x5 = -15x + 15x + 11x3 + -11x3 Combine like terms: -15x + 15x = 0 27x + -21x3 + 2x5 = 0 + 11x3 + -11x3 27x + -21x3 + 2x5 = 11x3 + -11x3 Combine like terms: 11x3 + -11x3 = 0 27x + -21x3 + 2x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(27 + -21x2 + 2x4) = 0 Factor a trinomial. x((3 + -2x2)(9 + -1x2)) = 0 Factor a difference between two squares. x((3 + -2x2)((3 + 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 '(3 + -2x2)' equal to zero and attempt to solve: Simplifying 3 + -2x2 = 0 Solving 3 + -2x2 = 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 + -2x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x2 = 0 + -3 -2x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2x2 = -3 Divide each side by '-2'. x2 = 1.5 Simplifying x2 = 1.5 Take the square root of each side: x = {-1.224744871, 1.224744871}Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 4
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, -1.224744871, 1.224744871, -3, 3}
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