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Simplifying 15x3 = 10x2 + 40x Reorder the terms: 15x3 = 40x + 10x2 Solving 15x3 = 40x + 10x2 Solving for variable 'x'. Reorder the terms: -40x + -10x2 + 15x3 = 40x + 10x2 + -40x + -10x2 Reorder the terms: -40x + -10x2 + 15x3 = 40x + -40x + 10x2 + -10x2 Combine like terms: 40x + -40x = 0 -40x + -10x2 + 15x3 = 0 + 10x2 + -10x2 -40x + -10x2 + 15x3 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -40x + -10x2 + 15x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-8 + -2x + 3x2) = 0 Factor a trinomial. 5x((-4 + -3x)(2 + -1x)) = 0 Ignore the factor 5.Subproblem 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 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0, -1.333333333, 2}
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