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Simplifying (x + 3)(5 + -1x) + (x + 3)(2x + -1) = 0 Reorder the terms: (3 + x)(5 + -1x) + (x + 3)(2x + -1) = 0 Multiply (3 + x) * (5 + -1x) (3(5 + -1x) + x(5 + -1x)) + (x + 3)(2x + -1) = 0 ((5 * 3 + -1x * 3) + x(5 + -1x)) + (x + 3)(2x + -1) = 0 ((15 + -3x) + x(5 + -1x)) + (x + 3)(2x + -1) = 0 (15 + -3x + (5 * x + -1x * x)) + (x + 3)(2x + -1) = 0 (15 + -3x + (5x + -1x2)) + (x + 3)(2x + -1) = 0 Combine like terms: -3x + 5x = 2x (15 + 2x + -1x2) + (x + 3)(2x + -1) = 0 Reorder the terms: 15 + 2x + -1x2 + (3 + x)(2x + -1) = 0 Reorder the terms: 15 + 2x + -1x2 + (3 + x)(-1 + 2x) = 0 Multiply (3 + x) * (-1 + 2x) 15 + 2x + -1x2 + (3(-1 + 2x) + x(-1 + 2x)) = 0 15 + 2x + -1x2 + ((-1 * 3 + 2x * 3) + x(-1 + 2x)) = 0 15 + 2x + -1x2 + ((-3 + 6x) + x(-1 + 2x)) = 0 15 + 2x + -1x2 + (-3 + 6x + (-1 * x + 2x * x)) = 0 15 + 2x + -1x2 + (-3 + 6x + (-1x + 2x2)) = 0 Combine like terms: 6x + -1x = 5x 15 + 2x + -1x2 + (-3 + 5x + 2x2) = 0 Reorder the terms: 15 + -3 + 2x + 5x + -1x2 + 2x2 = 0 Combine like terms: 15 + -3 = 12 12 + 2x + 5x + -1x2 + 2x2 = 0 Combine like terms: 2x + 5x = 7x 12 + 7x + -1x2 + 2x2 = 0 Combine like terms: -1x2 + 2x2 = 1x2 12 + 7x + 1x2 = 0 Solving 12 + 7x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (4 + x)(3 + x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-4, -3}
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