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Simplifying 0 = 12x2 + 17x + 6 Reorder the terms: 0 = 6 + 17x + 12x2 Solving 0 = 6 + 17x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -17x + -12x2 = 6 + 17x + 12x2 + -6 + -17x + -12x2 Reorder the terms: -6 + -17x + -12x2 = 6 + -6 + 17x + -17x + 12x2 + -12x2 Combine like terms: 6 + -6 = 0 -6 + -17x + -12x2 = 0 + 17x + -17x + 12x2 + -12x2 -6 + -17x + -12x2 = 17x + -17x + 12x2 + -12x2 Combine like terms: 17x + -17x = 0 -6 + -17x + -12x2 = 0 + 12x2 + -12x2 -6 + -17x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -6 + -17x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 17x + 12x2) = 0 Factor a trinomial. -1((3 + 4x)(2 + 3x)) = 0 Ignore the factor -1.Subproblem 1
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 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 = -0.6666666667Solution
x = {-0.75, -0.6666666667}
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