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Simplifying -6x2 = 13x + 6 Reorder the terms: -6x2 = 6 + 13x Solving -6x2 = 6 + 13x Solving for variable 'x'. Reorder the terms: -6 + -13x + -6x2 = 6 + 13x + -6 + -13x Reorder the terms: -6 + -13x + -6x2 = 6 + -6 + 13x + -13x Combine like terms: 6 + -6 = 0 -6 + -13x + -6x2 = 0 + 13x + -13x -6 + -13x + -6x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -6 + -13x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 13x + 6x2) = 0 Factor a trinomial. -1((3 + 2x)(2 + 3x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, -0.6666666667}
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