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Simplifying (x + -4)(x + 7) + (x + -4)(x + 6) = 0 Reorder the terms: (-4 + x)(x + 7) + (x + -4)(x + 6) = 0 Reorder the terms: (-4 + x)(7 + x) + (x + -4)(x + 6) = 0 Multiply (-4 + x) * (7 + x) (-4(7 + x) + x(7 + x)) + (x + -4)(x + 6) = 0 ((7 * -4 + x * -4) + x(7 + x)) + (x + -4)(x + 6) = 0 ((-28 + -4x) + x(7 + x)) + (x + -4)(x + 6) = 0 (-28 + -4x + (7 * x + x * x)) + (x + -4)(x + 6) = 0 (-28 + -4x + (7x + x2)) + (x + -4)(x + 6) = 0 Combine like terms: -4x + 7x = 3x (-28 + 3x + x2) + (x + -4)(x + 6) = 0 Reorder the terms: -28 + 3x + x2 + (-4 + x)(x + 6) = 0 Reorder the terms: -28 + 3x + x2 + (-4 + x)(6 + x) = 0 Multiply (-4 + x) * (6 + x) -28 + 3x + x2 + (-4(6 + x) + x(6 + x)) = 0 -28 + 3x + x2 + ((6 * -4 + x * -4) + x(6 + x)) = 0 -28 + 3x + x2 + ((-24 + -4x) + x(6 + x)) = 0 -28 + 3x + x2 + (-24 + -4x + (6 * x + x * x)) = 0 -28 + 3x + x2 + (-24 + -4x + (6x + x2)) = 0 Combine like terms: -4x + 6x = 2x -28 + 3x + x2 + (-24 + 2x + x2) = 0 Reorder the terms: -28 + -24 + 3x + 2x + x2 + x2 = 0 Combine like terms: -28 + -24 = -52 -52 + 3x + 2x + x2 + x2 = 0 Combine like terms: 3x + 2x = 5x -52 + 5x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -52 + 5x + 2x2 = 0 Solving -52 + 5x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-13 + -2x)(4 + -1x) = 0Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve: Simplifying -13 + -2x = 0 Solving -13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2x = 0 + 13 -2x = 0 + 13 Combine like terms: 0 + 13 = 13 -2x = 13 Divide each side by '-2'. x = -6.5 Simplifying x = -6.5Subproblem 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 = {-6.5, 4}
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