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Simplifying (3x + 7)(x + -8) + -1(2x + 1)(x + -5) = 2x + 5 Reorder the terms: (7 + 3x)(x + -8) + -1(2x + 1)(x + -5) = 2x + 5 Reorder the terms: (7 + 3x)(-8 + x) + -1(2x + 1)(x + -5) = 2x + 5 Multiply (7 + 3x) * (-8 + x) (7(-8 + x) + 3x * (-8 + x)) + -1(2x + 1)(x + -5) = 2x + 5 ((-8 * 7 + x * 7) + 3x * (-8 + x)) + -1(2x + 1)(x + -5) = 2x + 5 ((-56 + 7x) + 3x * (-8 + x)) + -1(2x + 1)(x + -5) = 2x + 5 (-56 + 7x + (-8 * 3x + x * 3x)) + -1(2x + 1)(x + -5) = 2x + 5 (-56 + 7x + (-24x + 3x2)) + -1(2x + 1)(x + -5) = 2x + 5 Combine like terms: 7x + -24x = -17x (-56 + -17x + 3x2) + -1(2x + 1)(x + -5) = 2x + 5 Reorder the terms: -56 + -17x + 3x2 + -1(1 + 2x)(x + -5) = 2x + 5 Reorder the terms: -56 + -17x + 3x2 + -1(1 + 2x)(-5 + x) = 2x + 5 Multiply (1 + 2x) * (-5 + x) -56 + -17x + 3x2 + -1(1(-5 + x) + 2x * (-5 + x)) = 2x + 5 -56 + -17x + 3x2 + -1((-5 * 1 + x * 1) + 2x * (-5 + x)) = 2x + 5 -56 + -17x + 3x2 + -1((-5 + 1x) + 2x * (-5 + x)) = 2x + 5 -56 + -17x + 3x2 + -1(-5 + 1x + (-5 * 2x + x * 2x)) = 2x + 5 -56 + -17x + 3x2 + -1(-5 + 1x + (-10x + 2x2)) = 2x + 5 Combine like terms: 1x + -10x = -9x -56 + -17x + 3x2 + -1(-5 + -9x + 2x2) = 2x + 5 -56 + -17x + 3x2 + (-5 * -1 + -9x * -1 + 2x2 * -1) = 2x + 5 -56 + -17x + 3x2 + (5 + 9x + -2x2) = 2x + 5 Reorder the terms: -56 + 5 + -17x + 9x + 3x2 + -2x2 = 2x + 5 Combine like terms: -56 + 5 = -51 -51 + -17x + 9x + 3x2 + -2x2 = 2x + 5 Combine like terms: -17x + 9x = -8x -51 + -8x + 3x2 + -2x2 = 2x + 5 Combine like terms: 3x2 + -2x2 = 1x2 -51 + -8x + 1x2 = 2x + 5 Reorder the terms: -51 + -8x + 1x2 = 5 + 2x Solving -51 + -8x + 1x2 = 5 + 2x Solving for variable 'x'. Reorder the terms: -51 + -5 + -8x + -2x + 1x2 = 5 + 2x + -5 + -2x Combine like terms: -51 + -5 = -56 -56 + -8x + -2x + 1x2 = 5 + 2x + -5 + -2x Combine like terms: -8x + -2x = -10x -56 + -10x + 1x2 = 5 + 2x + -5 + -2x Reorder the terms: -56 + -10x + 1x2 = 5 + -5 + 2x + -2x Combine like terms: 5 + -5 = 0 -56 + -10x + 1x2 = 0 + 2x + -2x -56 + -10x + 1x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -56 + -10x + 1x2 = 0 Factor a trinomial. (-4 + -1x)(14 + -1x) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {-4, 14}
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