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Simplifying (x + -4)(x + 3) + (x + -4)(x + 8) = 0 Reorder the terms: (-4 + x)(x + 3) + (x + -4)(x + 8) = 0 Reorder the terms: (-4 + x)(3 + x) + (x + -4)(x + 8) = 0 Multiply (-4 + x) * (3 + x) (-4(3 + x) + x(3 + x)) + (x + -4)(x + 8) = 0 ((3 * -4 + x * -4) + x(3 + x)) + (x + -4)(x + 8) = 0 ((-12 + -4x) + x(3 + x)) + (x + -4)(x + 8) = 0 (-12 + -4x + (3 * x + x * x)) + (x + -4)(x + 8) = 0 (-12 + -4x + (3x + x2)) + (x + -4)(x + 8) = 0 Combine like terms: -4x + 3x = -1x (-12 + -1x + x2) + (x + -4)(x + 8) = 0 Reorder the terms: -12 + -1x + x2 + (-4 + x)(x + 8) = 0 Reorder the terms: -12 + -1x + x2 + (-4 + x)(8 + x) = 0 Multiply (-4 + x) * (8 + x) -12 + -1x + x2 + (-4(8 + x) + x(8 + x)) = 0 -12 + -1x + x2 + ((8 * -4 + x * -4) + x(8 + x)) = 0 -12 + -1x + x2 + ((-32 + -4x) + x(8 + x)) = 0 -12 + -1x + x2 + (-32 + -4x + (8 * x + x * x)) = 0 -12 + -1x + x2 + (-32 + -4x + (8x + x2)) = 0 Combine like terms: -4x + 8x = 4x -12 + -1x + x2 + (-32 + 4x + x2) = 0 Reorder the terms: -12 + -32 + -1x + 4x + x2 + x2 = 0 Combine like terms: -12 + -32 = -44 -44 + -1x + 4x + x2 + x2 = 0 Combine like terms: -1x + 4x = 3x -44 + 3x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -44 + 3x + 2x2 = 0 Solving -44 + 3x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-11 + -2x)(4 + -1x) = 0Subproblem 1
Set the factor '(-11 + -2x)' equal to zero and attempt to solve: Simplifying -11 + -2x = 0 Solving -11 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2x = 0 + 11 -2x = 0 + 11 Combine like terms: 0 + 11 = 11 -2x = 11 Divide each side by '-2'. x = -5.5 Simplifying x = -5.5Subproblem 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 = {-5.5, 4}
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