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Simplifying 12x3 + 14x2 + 8x = 4x Reorder the terms: 8x + 14x2 + 12x3 = 4x Solving 8x + 14x2 + 12x3 = 4x Solving for variable 'x'. Reorder the terms: 8x + -4x + 14x2 + 12x3 = 4x + -4x Combine like terms: 8x + -4x = 4x 4x + 14x2 + 12x3 = 4x + -4x Combine like terms: 4x + -4x = 0 4x + 14x2 + 12x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(2 + 7x + 6x2) = 0 Factor a trinomial. 2x((2 + 3x)(1 + 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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 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, -0.6666666667, -0.5}
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