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Simplifying 0 = 4x3 + -42x2 + 108x Reorder the terms: 0 = 108x + -42x2 + 4x3 Solving 0 = 108x + -42x2 + 4x3 Solving for variable 'x'. Remove the zero: -108x + 42x2 + -4x3 = 108x + -42x2 + 4x3 + -108x + 42x2 + -4x3 Reorder the terms: -108x + 42x2 + -4x3 = 108x + -108x + -42x2 + 42x2 + 4x3 + -4x3 Combine like terms: 108x + -108x = 0 -108x + 42x2 + -4x3 = 0 + -42x2 + 42x2 + 4x3 + -4x3 -108x + 42x2 + -4x3 = -42x2 + 42x2 + 4x3 + -4x3 Combine like terms: -42x2 + 42x2 = 0 -108x + 42x2 + -4x3 = 0 + 4x3 + -4x3 -108x + 42x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -108x + 42x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-54 + 21x + -2x2) = 0 Factor a trinomial. 2x((-6 + x)(9 + -2x)) = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 3
Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {0, 6, 4.5}
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