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Simplifying 0 = (3x + -6)(2x + 7) Reorder the terms: 0 = (-6 + 3x)(2x + 7) Reorder the terms: 0 = (-6 + 3x)(7 + 2x) Multiply (-6 + 3x) * (7 + 2x) 0 = (-6(7 + 2x) + 3x * (7 + 2x)) 0 = ((7 * -6 + 2x * -6) + 3x * (7 + 2x)) 0 = ((-42 + -12x) + 3x * (7 + 2x)) 0 = (-42 + -12x + (7 * 3x + 2x * 3x)) 0 = (-42 + -12x + (21x + 6x2)) Combine like terms: -12x + 21x = 9x 0 = (-42 + 9x + 6x2) Solving 0 = -42 + 9x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 42 = 42 42 + -9x + -6x2 = -42 + 9x + 6x2 + 42 + -9x + -6x2 Reorder the terms: 42 + -9x + -6x2 = -42 + 42 + 9x + -9x + 6x2 + -6x2 Combine like terms: -42 + 42 = 0 42 + -9x + -6x2 = 0 + 9x + -9x + 6x2 + -6x2 42 + -9x + -6x2 = 9x + -9x + 6x2 + -6x2 Combine like terms: 9x + -9x = 0 42 + -9x + -6x2 = 0 + 6x2 + -6x2 42 + -9x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 42 + -9x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -3x + -2x2) = 0 Factor a trinomial. 3((2 + -1x)(7 + 2x)) = 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 '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Solution
x = {2, -3.5}
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