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Simplifying 24x3 = -10x2 + 6x Reorder the terms: 24x3 = 6x + -10x2 Solving 24x3 = 6x + -10x2 Solving for variable 'x'. Reorder the terms: -6x + 10x2 + 24x3 = 6x + -10x2 + -6x + 10x2 Reorder the terms: -6x + 10x2 + 24x3 = 6x + -6x + -10x2 + 10x2 Combine like terms: 6x + -6x = 0 -6x + 10x2 + 24x3 = 0 + -10x2 + 10x2 -6x + 10x2 + 24x3 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -6x + 10x2 + 24x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + 5x + 12x2) = 0 Factor a trinomial. 2x((-3 + -4x)(1 + -3x)) = 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 '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 3
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 = 0.3333333333Solution
x = {0, -0.75, 0.3333333333}
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