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Simplifying 8x3 = 6x2 + 5x Reorder the terms: 8x3 = 5x + 6x2 Solving 8x3 = 5x + 6x2 Solving for variable 'x'. Reorder the terms: -5x + -6x2 + 8x3 = 5x + 6x2 + -5x + -6x2 Reorder the terms: -5x + -6x2 + 8x3 = 5x + -5x + 6x2 + -6x2 Combine like terms: 5x + -5x = 0 -5x + -6x2 + 8x3 = 0 + 6x2 + -6x2 -5x + -6x2 + 8x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -5x + -6x2 + 8x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + -6x + 8x2) = 0 Factor a trinomial. x((-1 + -2x)(5 + -4x)) = 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 + -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 = -0.5Subproblem 3
Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Solution
x = {0, -0.5, 1.25}
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