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Simplifying (x + 1)(x + -3) + (x + 1)(2x + 4) = 0 Reorder the terms: (1 + x)(x + -3) + (x + 1)(2x + 4) = 0 Reorder the terms: (1 + x)(-3 + x) + (x + 1)(2x + 4) = 0 Multiply (1 + x) * (-3 + x) (1(-3 + x) + x(-3 + x)) + (x + 1)(2x + 4) = 0 ((-3 * 1 + x * 1) + x(-3 + x)) + (x + 1)(2x + 4) = 0 ((-3 + 1x) + x(-3 + x)) + (x + 1)(2x + 4) = 0 (-3 + 1x + (-3 * x + x * x)) + (x + 1)(2x + 4) = 0 (-3 + 1x + (-3x + x2)) + (x + 1)(2x + 4) = 0 Combine like terms: 1x + -3x = -2x (-3 + -2x + x2) + (x + 1)(2x + 4) = 0 Reorder the terms: -3 + -2x + x2 + (1 + x)(2x + 4) = 0 Reorder the terms: -3 + -2x + x2 + (1 + x)(4 + 2x) = 0 Multiply (1 + x) * (4 + 2x) -3 + -2x + x2 + (1(4 + 2x) + x(4 + 2x)) = 0 -3 + -2x + x2 + ((4 * 1 + 2x * 1) + x(4 + 2x)) = 0 -3 + -2x + x2 + ((4 + 2x) + x(4 + 2x)) = 0 -3 + -2x + x2 + (4 + 2x + (4 * x + 2x * x)) = 0 -3 + -2x + x2 + (4 + 2x + (4x + 2x2)) = 0 Combine like terms: 2x + 4x = 6x -3 + -2x + x2 + (4 + 6x + 2x2) = 0 Reorder the terms: -3 + 4 + -2x + 6x + x2 + 2x2 = 0 Combine like terms: -3 + 4 = 1 1 + -2x + 6x + x2 + 2x2 = 0 Combine like terms: -2x + 6x = 4x 1 + 4x + x2 + 2x2 = 0 Combine like terms: x2 + 2x2 = 3x2 1 + 4x + 3x2 = 0 Solving 1 + 4x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + x)(1 + 3x) = 0Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-1, -0.3333333333}
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