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Simplifying (x + 1)(x + -2) + -3(x + 5) = 3 + -5x Reorder the terms: (1 + x)(x + -2) + -3(x + 5) = 3 + -5x Reorder the terms: (1 + x)(-2 + x) + -3(x + 5) = 3 + -5x Multiply (1 + x) * (-2 + x) (1(-2 + x) + x(-2 + x)) + -3(x + 5) = 3 + -5x ((-2 * 1 + x * 1) + x(-2 + x)) + -3(x + 5) = 3 + -5x ((-2 + 1x) + x(-2 + x)) + -3(x + 5) = 3 + -5x (-2 + 1x + (-2 * x + x * x)) + -3(x + 5) = 3 + -5x (-2 + 1x + (-2x + x2)) + -3(x + 5) = 3 + -5x Combine like terms: 1x + -2x = -1x (-2 + -1x + x2) + -3(x + 5) = 3 + -5x Reorder the terms: -2 + -1x + x2 + -3(5 + x) = 3 + -5x -2 + -1x + x2 + (5 * -3 + x * -3) = 3 + -5x -2 + -1x + x2 + (-15 + -3x) = 3 + -5x Reorder the terms: -2 + -15 + -1x + -3x + x2 = 3 + -5x Combine like terms: -2 + -15 = -17 -17 + -1x + -3x + x2 = 3 + -5x Combine like terms: -1x + -3x = -4x -17 + -4x + x2 = 3 + -5x Solving -17 + -4x + x2 = 3 + -5x Solving for variable 'x'. Reorder the terms: -17 + -3 + -4x + 5x + x2 = 3 + -5x + -3 + 5x Combine like terms: -17 + -3 = -20 -20 + -4x + 5x + x2 = 3 + -5x + -3 + 5x Combine like terms: -4x + 5x = 1x -20 + 1x + x2 = 3 + -5x + -3 + 5x Reorder the terms: -20 + 1x + x2 = 3 + -3 + -5x + 5x Combine like terms: 3 + -3 = 0 -20 + 1x + x2 = 0 + -5x + 5x -20 + 1x + x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -20 + 1x + x2 = 0 Factor a trinomial. (-5 + -1x)(4 + -1x) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-5, 4}
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