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Simplifying (x + 3)(x + -2) = 204 Reorder the terms: (3 + x)(x + -2) = 204 Reorder the terms: (3 + x)(-2 + x) = 204 Multiply (3 + x) * (-2 + x) (3(-2 + x) + x(-2 + x)) = 204 ((-2 * 3 + x * 3) + x(-2 + x)) = 204 ((-6 + 3x) + x(-2 + x)) = 204 (-6 + 3x + (-2 * x + x * x)) = 204 (-6 + 3x + (-2x + x2)) = 204 Combine like terms: 3x + -2x = 1x (-6 + 1x + x2) = 204 Solving -6 + 1x + x2 = 204 Solving for variable 'x'. Reorder the terms: -6 + -204 + 1x + x2 = 204 + -204 Combine like terms: -6 + -204 = -210 -210 + 1x + x2 = 204 + -204 Combine like terms: 204 + -204 = 0 -210 + 1x + x2 = 0 Factor a trinomial. (-15 + -1x)(14 + -1x) = 0Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 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 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {-15, 14}
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