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Simplifying 5x2 + -15x + 18 = 2x2 + 6x + -12 Reorder the terms: 18 + -15x + 5x2 = 2x2 + 6x + -12 Reorder the terms: 18 + -15x + 5x2 = -12 + 6x + 2x2 Solving 18 + -15x + 5x2 = -12 + 6x + 2x2 Solving for variable 'x'. Reorder the terms: 18 + 12 + -15x + -6x + 5x2 + -2x2 = -12 + 6x + 2x2 + 12 + -6x + -2x2 Combine like terms: 18 + 12 = 30 30 + -15x + -6x + 5x2 + -2x2 = -12 + 6x + 2x2 + 12 + -6x + -2x2 Combine like terms: -15x + -6x = -21x 30 + -21x + 5x2 + -2x2 = -12 + 6x + 2x2 + 12 + -6x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 30 + -21x + 3x2 = -12 + 6x + 2x2 + 12 + -6x + -2x2 Reorder the terms: 30 + -21x + 3x2 = -12 + 12 + 6x + -6x + 2x2 + -2x2 Combine like terms: -12 + 12 = 0 30 + -21x + 3x2 = 0 + 6x + -6x + 2x2 + -2x2 30 + -21x + 3x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 30 + -21x + 3x2 = 0 + 2x2 + -2x2 30 + -21x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 30 + -21x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -7x + x2) = 0 Factor a trinomial. 3((2 + -1x)(5 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {2, 5}
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