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Simplifying (x + 3)(x + -5) + (7 + -2x)(1 + -1x) = 12 Reorder the terms: (3 + x)(x + -5) + (7 + -2x)(1 + -1x) = 12 Reorder the terms: (3 + x)(-5 + x) + (7 + -2x)(1 + -1x) = 12 Multiply (3 + x) * (-5 + x) (3(-5 + x) + x(-5 + x)) + (7 + -2x)(1 + -1x) = 12 ((-5 * 3 + x * 3) + x(-5 + x)) + (7 + -2x)(1 + -1x) = 12 ((-15 + 3x) + x(-5 + x)) + (7 + -2x)(1 + -1x) = 12 (-15 + 3x + (-5 * x + x * x)) + (7 + -2x)(1 + -1x) = 12 (-15 + 3x + (-5x + x2)) + (7 + -2x)(1 + -1x) = 12 Combine like terms: 3x + -5x = -2x (-15 + -2x + x2) + (7 + -2x)(1 + -1x) = 12 Multiply (7 + -2x) * (1 + -1x) -15 + -2x + x2 + (7(1 + -1x) + -2x * (1 + -1x)) = 12 -15 + -2x + x2 + ((1 * 7 + -1x * 7) + -2x * (1 + -1x)) = 12 -15 + -2x + x2 + ((7 + -7x) + -2x * (1 + -1x)) = 12 -15 + -2x + x2 + (7 + -7x + (1 * -2x + -1x * -2x)) = 12 -15 + -2x + x2 + (7 + -7x + (-2x + 2x2)) = 12 Combine like terms: -7x + -2x = -9x -15 + -2x + x2 + (7 + -9x + 2x2) = 12 Reorder the terms: -15 + 7 + -2x + -9x + x2 + 2x2 = 12 Combine like terms: -15 + 7 = -8 -8 + -2x + -9x + x2 + 2x2 = 12 Combine like terms: -2x + -9x = -11x -8 + -11x + x2 + 2x2 = 12 Combine like terms: x2 + 2x2 = 3x2 -8 + -11x + 3x2 = 12 Solving -8 + -11x + 3x2 = 12 Solving for variable 'x'. Reorder the terms: -8 + -12 + -11x + 3x2 = 12 + -12 Combine like terms: -8 + -12 = -20 -20 + -11x + 3x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -20 + -11x + 3x2 = 0 Factor a trinomial. (-4 + -3x)(5 + -1x) = 0Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 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 = {-1.333333333, 5}
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