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Simplifying (2x + -3)(x + -9) + 18 = 0 Reorder the terms: (-3 + 2x)(x + -9) + 18 = 0 Reorder the terms: (-3 + 2x)(-9 + x) + 18 = 0 Multiply (-3 + 2x) * (-9 + x) (-3(-9 + x) + 2x * (-9 + x)) + 18 = 0 ((-9 * -3 + x * -3) + 2x * (-9 + x)) + 18 = 0 ((27 + -3x) + 2x * (-9 + x)) + 18 = 0 (27 + -3x + (-9 * 2x + x * 2x)) + 18 = 0 (27 + -3x + (-18x + 2x2)) + 18 = 0 Combine like terms: -3x + -18x = -21x (27 + -21x + 2x2) + 18 = 0 Reorder the terms: 27 + 18 + -21x + 2x2 = 0 Combine like terms: 27 + 18 = 45 45 + -21x + 2x2 = 0 Solving 45 + -21x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -1x)(15 + -2x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(15 + -2x)' equal to zero and attempt to solve: Simplifying 15 + -2x = 0 Solving 15 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2x = 0 + -15 -2x = 0 + -15 Combine like terms: 0 + -15 = -15 -2x = -15 Divide each side by '-2'. x = 7.5 Simplifying x = 7.5Solution
x = {3, 7.5}
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