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Simplifying (5x + -4)(x + 9) = (x + 8)(6x + -6) Reorder the terms: (-4 + 5x)(x + 9) = (x + 8)(6x + -6) Reorder the terms: (-4 + 5x)(9 + x) = (x + 8)(6x + -6) Multiply (-4 + 5x) * (9 + x) (-4(9 + x) + 5x * (9 + x)) = (x + 8)(6x + -6) ((9 * -4 + x * -4) + 5x * (9 + x)) = (x + 8)(6x + -6) ((-36 + -4x) + 5x * (9 + x)) = (x + 8)(6x + -6) (-36 + -4x + (9 * 5x + x * 5x)) = (x + 8)(6x + -6) (-36 + -4x + (45x + 5x2)) = (x + 8)(6x + -6) Combine like terms: -4x + 45x = 41x (-36 + 41x + 5x2) = (x + 8)(6x + -6) Reorder the terms: -36 + 41x + 5x2 = (8 + x)(6x + -6) Reorder the terms: -36 + 41x + 5x2 = (8 + x)(-6 + 6x) Multiply (8 + x) * (-6 + 6x) -36 + 41x + 5x2 = (8(-6 + 6x) + x(-6 + 6x)) -36 + 41x + 5x2 = ((-6 * 8 + 6x * 8) + x(-6 + 6x)) -36 + 41x + 5x2 = ((-48 + 48x) + x(-6 + 6x)) -36 + 41x + 5x2 = (-48 + 48x + (-6 * x + 6x * x)) -36 + 41x + 5x2 = (-48 + 48x + (-6x + 6x2)) Combine like terms: 48x + -6x = 42x -36 + 41x + 5x2 = (-48 + 42x + 6x2) Solving -36 + 41x + 5x2 = -48 + 42x + 6x2 Solving for variable 'x'. Reorder the terms: -36 + 48 + 41x + -42x + 5x2 + -6x2 = -48 + 42x + 6x2 + 48 + -42x + -6x2 Combine like terms: -36 + 48 = 12 12 + 41x + -42x + 5x2 + -6x2 = -48 + 42x + 6x2 + 48 + -42x + -6x2 Combine like terms: 41x + -42x = -1x 12 + -1x + 5x2 + -6x2 = -48 + 42x + 6x2 + 48 + -42x + -6x2 Combine like terms: 5x2 + -6x2 = -1x2 12 + -1x + -1x2 = -48 + 42x + 6x2 + 48 + -42x + -6x2 Reorder the terms: 12 + -1x + -1x2 = -48 + 48 + 42x + -42x + 6x2 + -6x2 Combine like terms: -48 + 48 = 0 12 + -1x + -1x2 = 0 + 42x + -42x + 6x2 + -6x2 12 + -1x + -1x2 = 42x + -42x + 6x2 + -6x2 Combine like terms: 42x + -42x = 0 12 + -1x + -1x2 = 0 + 6x2 + -6x2 12 + -1x + -1x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 12 + -1x + -1x2 = 0 Factor a trinomial. (3 + -1x)(4 + x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
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 = -4Solution
x = {3, -4}
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