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Simplifying (x + -2)(x + 4) + (x + -2)(3x + 1) = 0 Reorder the terms: (-2 + x)(x + 4) + (x + -2)(3x + 1) = 0 Reorder the terms: (-2 + x)(4 + x) + (x + -2)(3x + 1) = 0 Multiply (-2 + x) * (4 + x) (-2(4 + x) + x(4 + x)) + (x + -2)(3x + 1) = 0 ((4 * -2 + x * -2) + x(4 + x)) + (x + -2)(3x + 1) = 0 ((-8 + -2x) + x(4 + x)) + (x + -2)(3x + 1) = 0 (-8 + -2x + (4 * x + x * x)) + (x + -2)(3x + 1) = 0 (-8 + -2x + (4x + x2)) + (x + -2)(3x + 1) = 0 Combine like terms: -2x + 4x = 2x (-8 + 2x + x2) + (x + -2)(3x + 1) = 0 Reorder the terms: -8 + 2x + x2 + (-2 + x)(3x + 1) = 0 Reorder the terms: -8 + 2x + x2 + (-2 + x)(1 + 3x) = 0 Multiply (-2 + x) * (1 + 3x) -8 + 2x + x2 + (-2(1 + 3x) + x(1 + 3x)) = 0 -8 + 2x + x2 + ((1 * -2 + 3x * -2) + x(1 + 3x)) = 0 -8 + 2x + x2 + ((-2 + -6x) + x(1 + 3x)) = 0 -8 + 2x + x2 + (-2 + -6x + (1 * x + 3x * x)) = 0 -8 + 2x + x2 + (-2 + -6x + (1x + 3x2)) = 0 Combine like terms: -6x + 1x = -5x -8 + 2x + x2 + (-2 + -5x + 3x2) = 0 Reorder the terms: -8 + -2 + 2x + -5x + x2 + 3x2 = 0 Combine like terms: -8 + -2 = -10 -10 + 2x + -5x + x2 + 3x2 = 0 Combine like terms: 2x + -5x = -3x -10 + -3x + x2 + 3x2 = 0 Combine like terms: x2 + 3x2 = 4x2 -10 + -3x + 4x2 = 0 Solving -10 + -3x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -4x)(2 + -1x) = 0Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 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 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-1.25, 2}
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