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Simplifying x + -6 = 4x(x + 3) Reorder the terms: -6 + x = 4x(x + 3) Reorder the terms: -6 + x = 4x(3 + x) -6 + x = (3 * 4x + x * 4x) -6 + x = (12x + 4x2) Solving -6 + x = 12x + 4x2 Solving for variable 'x'. Combine like terms: x + -12x = -11x -6 + -11x + -4x2 = 12x + 4x2 + -12x + -4x2 Reorder the terms: -6 + -11x + -4x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 -6 + -11x + -4x2 = 0 + 4x2 + -4x2 -6 + -11x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -6 + -11x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 11x + 4x2) = 0 Factor a trinomial. -1((2 + x)(3 + 4x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 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 = -0.75Solution
x = {-2, -0.75}
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