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Simplifying (x + 8)(x + -3) = (2x + 7)(x + -3) Reorder the terms: (8 + x)(x + -3) = (2x + 7)(x + -3) Reorder the terms: (8 + x)(-3 + x) = (2x + 7)(x + -3) Multiply (8 + x) * (-3 + x) (8(-3 + x) + x(-3 + x)) = (2x + 7)(x + -3) ((-3 * 8 + x * 8) + x(-3 + x)) = (2x + 7)(x + -3) ((-24 + 8x) + x(-3 + x)) = (2x + 7)(x + -3) (-24 + 8x + (-3 * x + x * x)) = (2x + 7)(x + -3) (-24 + 8x + (-3x + x2)) = (2x + 7)(x + -3) Combine like terms: 8x + -3x = 5x (-24 + 5x + x2) = (2x + 7)(x + -3) Reorder the terms: -24 + 5x + x2 = (7 + 2x)(x + -3) Reorder the terms: -24 + 5x + x2 = (7 + 2x)(-3 + x) Multiply (7 + 2x) * (-3 + x) -24 + 5x + x2 = (7(-3 + x) + 2x * (-3 + x)) -24 + 5x + x2 = ((-3 * 7 + x * 7) + 2x * (-3 + x)) -24 + 5x + x2 = ((-21 + 7x) + 2x * (-3 + x)) -24 + 5x + x2 = (-21 + 7x + (-3 * 2x + x * 2x)) -24 + 5x + x2 = (-21 + 7x + (-6x + 2x2)) Combine like terms: 7x + -6x = 1x -24 + 5x + x2 = (-21 + 1x + 2x2) Solving -24 + 5x + x2 = -21 + 1x + 2x2 Solving for variable 'x'. Reorder the terms: -24 + 21 + 5x + -1x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Combine like terms: -24 + 21 = -3 -3 + 5x + -1x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Combine like terms: 5x + -1x = 4x -3 + 4x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -3 + 4x + -1x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Reorder the terms: -3 + 4x + -1x2 = -21 + 21 + 1x + -1x + 2x2 + -2x2 Combine like terms: -21 + 21 = 0 -3 + 4x + -1x2 = 0 + 1x + -1x + 2x2 + -2x2 -3 + 4x + -1x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 -3 + 4x + -1x2 = 0 + 2x2 + -2x2 -3 + 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3 + 4x + -1x2 = 0 Factor a trinomial. (-3 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {3, 1}
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