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Simplifying (x + -5)(x + 3) + (x + -5)(x + 6) = 0 Reorder the terms: (-5 + x)(x + 3) + (x + -5)(x + 6) = 0 Reorder the terms: (-5 + x)(3 + x) + (x + -5)(x + 6) = 0 Multiply (-5 + x) * (3 + x) (-5(3 + x) + x(3 + x)) + (x + -5)(x + 6) = 0 ((3 * -5 + x * -5) + x(3 + x)) + (x + -5)(x + 6) = 0 ((-15 + -5x) + x(3 + x)) + (x + -5)(x + 6) = 0 (-15 + -5x + (3 * x + x * x)) + (x + -5)(x + 6) = 0 (-15 + -5x + (3x + x2)) + (x + -5)(x + 6) = 0 Combine like terms: -5x + 3x = -2x (-15 + -2x + x2) + (x + -5)(x + 6) = 0 Reorder the terms: -15 + -2x + x2 + (-5 + x)(x + 6) = 0 Reorder the terms: -15 + -2x + x2 + (-5 + x)(6 + x) = 0 Multiply (-5 + x) * (6 + x) -15 + -2x + x2 + (-5(6 + x) + x(6 + x)) = 0 -15 + -2x + x2 + ((6 * -5 + x * -5) + x(6 + x)) = 0 -15 + -2x + x2 + ((-30 + -5x) + x(6 + x)) = 0 -15 + -2x + x2 + (-30 + -5x + (6 * x + x * x)) = 0 -15 + -2x + x2 + (-30 + -5x + (6x + x2)) = 0 Combine like terms: -5x + 6x = 1x -15 + -2x + x2 + (-30 + 1x + x2) = 0 Reorder the terms: -15 + -30 + -2x + 1x + x2 + x2 = 0 Combine like terms: -15 + -30 = -45 -45 + -2x + 1x + x2 + x2 = 0 Combine like terms: -2x + 1x = -1x -45 + -1x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -45 + -1x + 2x2 = 0 Solving -45 + -1x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-9 + -2x)(5 + -1x) = 0Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 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 = {-4.5, 5}
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