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Simplifying 18x2 + 6x + 6 = 6x2 + 30x + -3 Reorder the terms: 6 + 6x + 18x2 = 6x2 + 30x + -3 Reorder the terms: 6 + 6x + 18x2 = -3 + 30x + 6x2 Solving 6 + 6x + 18x2 = -3 + 30x + 6x2 Solving for variable 'x'. Reorder the terms: 6 + 3 + 6x + -30x + 18x2 + -6x2 = -3 + 30x + 6x2 + 3 + -30x + -6x2 Combine like terms: 6 + 3 = 9 9 + 6x + -30x + 18x2 + -6x2 = -3 + 30x + 6x2 + 3 + -30x + -6x2 Combine like terms: 6x + -30x = -24x 9 + -24x + 18x2 + -6x2 = -3 + 30x + 6x2 + 3 + -30x + -6x2 Combine like terms: 18x2 + -6x2 = 12x2 9 + -24x + 12x2 = -3 + 30x + 6x2 + 3 + -30x + -6x2 Reorder the terms: 9 + -24x + 12x2 = -3 + 3 + 30x + -30x + 6x2 + -6x2 Combine like terms: -3 + 3 = 0 9 + -24x + 12x2 = 0 + 30x + -30x + 6x2 + -6x2 9 + -24x + 12x2 = 30x + -30x + 6x2 + -6x2 Combine like terms: 30x + -30x = 0 9 + -24x + 12x2 = 0 + 6x2 + -6x2 9 + -24x + 12x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 9 + -24x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -8x + 4x2) = 0 Factor a trinomial. 3((1 + -2x)(3 + -2x)) = 0 Ignore the factor 3.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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