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Simplifying -8x3 + 42x2 = 10x Reorder the terms: 42x2 + -8x3 = 10x Solving 42x2 + -8x3 = 10x Solving for variable 'x'. Reorder the terms: -10x + 42x2 + -8x3 = 10x + -10x Combine like terms: 10x + -10x = 0 -10x + 42x2 + -8x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-5 + 21x + -4x2) = 0 Factor a trinomial. 2x((-5 + x)(1 + -4x)) = 0 Ignore the factor 2.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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 3
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {0, 5, 0.25}
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