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Simplifying 24x3 = 4x2 + 4x Reorder the terms: 24x3 = 4x + 4x2 Solving 24x3 = 4x + 4x2 Solving for variable 'x'. Reorder the terms: -4x + -4x2 + 24x3 = 4x + 4x2 + -4x + -4x2 Reorder the terms: -4x + -4x2 + 24x3 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 -4x + -4x2 + 24x3 = 0 + 4x2 + -4x2 -4x + -4x2 + 24x3 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -4x + -4x2 + 24x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-1 + -1x + 6x2) = 0 Factor a trinomial. 4x((-1 + -3x)(1 + -2x)) = 0 Ignore the factor 4.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 '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 3
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 = 0.5Solution
x = {0, -0.3333333333, 0.5}
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