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Simplifying (6 + -2x)(7 + -2x) = 12 Multiply (6 + -2x) * (7 + -2x) (6(7 + -2x) + -2x * (7 + -2x)) = 12 ((7 * 6 + -2x * 6) + -2x * (7 + -2x)) = 12 ((42 + -12x) + -2x * (7 + -2x)) = 12 (42 + -12x + (7 * -2x + -2x * -2x)) = 12 (42 + -12x + (-14x + 4x2)) = 12 Combine like terms: -12x + -14x = -26x (42 + -26x + 4x2) = 12 Solving 42 + -26x + 4x2 = 12 Solving for variable 'x'. Reorder the terms: 42 + -12 + -26x + 4x2 = 12 + -12 Combine like terms: 42 + -12 = 30 30 + -26x + 4x2 = 12 + -12 Combine like terms: 12 + -12 = 0 30 + -26x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -13x + 2x2) = 0 Factor a trinomial. 2((3 + -2x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = 1.5Subproblem 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 = {1.5, 5}
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