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Simplifying (2x + 3)(x + 6) = 180 Reorder the terms: (3 + 2x)(x + 6) = 180 Reorder the terms: (3 + 2x)(6 + x) = 180 Multiply (3 + 2x) * (6 + x) (3(6 + x) + 2x * (6 + x)) = 180 ((6 * 3 + x * 3) + 2x * (6 + x)) = 180 ((18 + 3x) + 2x * (6 + x)) = 180 (18 + 3x + (6 * 2x + x * 2x)) = 180 (18 + 3x + (12x + 2x2)) = 180 Combine like terms: 3x + 12x = 15x (18 + 15x + 2x2) = 180 Solving 18 + 15x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 18 + -180 + 15x + 2x2 = 180 + -180 Combine like terms: 18 + -180 = -162 -162 + 15x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -162 + 15x + 2x2 = 0 Factor a trinomial. (-27 + -2x)(6 + -1x) = 0Subproblem 1
Set the factor '(-27 + -2x)' equal to zero and attempt to solve: Simplifying -27 + -2x = 0 Solving -27 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + -2x = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -2x = 0 + 27 -2x = 0 + 27 Combine like terms: 0 + 27 = 27 -2x = 27 Divide each side by '-2'. x = -13.5 Simplifying x = -13.5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-13.5, 6}
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