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Simplifying 3x + 2 = 12x2 + 5x Reorder the terms: 2 + 3x = 12x2 + 5x Reorder the terms: 2 + 3x = 5x + 12x2 Solving 2 + 3x = 5x + 12x2 Solving for variable 'x'. Combine like terms: 3x + -5x = -2x 2 + -2x + -12x2 = 5x + 12x2 + -5x + -12x2 Reorder the terms: 2 + -2x + -12x2 = 5x + -5x + 12x2 + -12x2 Combine like terms: 5x + -5x = 0 2 + -2x + -12x2 = 0 + 12x2 + -12x2 2 + -2x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 2 + -2x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -1x + -6x2) = 0 Factor a trinomial. 2((1 + -3x)(1 + 2x)) = 0 Ignore the factor 2.Subproblem 1
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 2
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 = {0.3333333333, -0.5}
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