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Simplifying 18x + 15 = 6x(2x + 3) + 6x + -3 Reorder the terms: 15 + 18x = 6x(2x + 3) + 6x + -3 Reorder the terms: 15 + 18x = 6x(3 + 2x) + 6x + -3 15 + 18x = (3 * 6x + 2x * 6x) + 6x + -3 15 + 18x = (18x + 12x2) + 6x + -3 Reorder the terms: 15 + 18x = -3 + 18x + 6x + 12x2 Combine like terms: 18x + 6x = 24x 15 + 18x = -3 + 24x + 12x2 Solving 15 + 18x = -3 + 24x + 12x2 Solving for variable 'x'. Reorder the terms: 15 + 3 + 18x + -24x + -12x2 = -3 + 24x + 12x2 + 3 + -24x + -12x2 Combine like terms: 15 + 3 = 18 18 + 18x + -24x + -12x2 = -3 + 24x + 12x2 + 3 + -24x + -12x2 Combine like terms: 18x + -24x = -6x 18 + -6x + -12x2 = -3 + 24x + 12x2 + 3 + -24x + -12x2 Reorder the terms: 18 + -6x + -12x2 = -3 + 3 + 24x + -24x + 12x2 + -12x2 Combine like terms: -3 + 3 = 0 18 + -6x + -12x2 = 0 + 24x + -24x + 12x2 + -12x2 18 + -6x + -12x2 = 24x + -24x + 12x2 + -12x2 Combine like terms: 24x + -24x = 0 18 + -6x + -12x2 = 0 + 12x2 + -12x2 18 + -6x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 18 + -6x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3 + -1x + -2x2) = 0 Factor a trinomial. 6((1 + -1x)(3 + 2x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 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 = {1, -1.5}
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