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Simplifying (x + 3)(x + -1) + (x + 2)(x + -1) = 0 Reorder the terms: (3 + x)(x + -1) + (x + 2)(x + -1) = 0 Reorder the terms: (3 + x)(-1 + x) + (x + 2)(x + -1) = 0 Multiply (3 + x) * (-1 + x) (3(-1 + x) + x(-1 + x)) + (x + 2)(x + -1) = 0 ((-1 * 3 + x * 3) + x(-1 + x)) + (x + 2)(x + -1) = 0 ((-3 + 3x) + x(-1 + x)) + (x + 2)(x + -1) = 0 (-3 + 3x + (-1 * x + x * x)) + (x + 2)(x + -1) = 0 (-3 + 3x + (-1x + x2)) + (x + 2)(x + -1) = 0 Combine like terms: 3x + -1x = 2x (-3 + 2x + x2) + (x + 2)(x + -1) = 0 Reorder the terms: -3 + 2x + x2 + (2 + x)(x + -1) = 0 Reorder the terms: -3 + 2x + x2 + (2 + x)(-1 + x) = 0 Multiply (2 + x) * (-1 + x) -3 + 2x + x2 + (2(-1 + x) + x(-1 + x)) = 0 -3 + 2x + x2 + ((-1 * 2 + x * 2) + x(-1 + x)) = 0 -3 + 2x + x2 + ((-2 + 2x) + x(-1 + x)) = 0 -3 + 2x + x2 + (-2 + 2x + (-1 * x + x * x)) = 0 -3 + 2x + x2 + (-2 + 2x + (-1x + x2)) = 0 Combine like terms: 2x + -1x = 1x -3 + 2x + x2 + (-2 + 1x + x2) = 0 Reorder the terms: -3 + -2 + 2x + 1x + x2 + x2 = 0 Combine like terms: -3 + -2 = -5 -5 + 2x + 1x + x2 + x2 = 0 Combine like terms: 2x + 1x = 3x -5 + 3x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -5 + 3x + 2x2 = 0 Solving -5 + 3x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -2x)(1 + -1x) = 0Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-2.5, 1}
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