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Simplifying 5x2 + -2x + -6 = -3x2 + 6x Reorder the terms: -6 + -2x + 5x2 = -3x2 + 6x Reorder the terms: -6 + -2x + 5x2 = 6x + -3x2 Solving -6 + -2x + 5x2 = 6x + -3x2 Solving for variable 'x'. Reorder the terms: -6 + -2x + -6x + 5x2 + 3x2 = 6x + -3x2 + -6x + 3x2 Combine like terms: -2x + -6x = -8x -6 + -8x + 5x2 + 3x2 = 6x + -3x2 + -6x + 3x2 Combine like terms: 5x2 + 3x2 = 8x2 -6 + -8x + 8x2 = 6x + -3x2 + -6x + 3x2 Reorder the terms: -6 + -8x + 8x2 = 6x + -6x + -3x2 + 3x2 Combine like terms: 6x + -6x = 0 -6 + -8x + 8x2 = 0 + -3x2 + 3x2 -6 + -8x + 8x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -6 + -8x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -4x + 4x2) = 0 Factor a trinomial. 2((-1 + -2x)(3 + -2x)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.5Subproblem 2
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 = 1.5Solution
x = {-0.5, 1.5}
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