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Simplifying (x + -8)(5x + 3) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) Reorder the terms: (-8 + x)(5x + 3) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) Reorder the terms: (-8 + x)(3 + 5x) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) Multiply (-8 + x) * (3 + 5x) (-8(3 + 5x) + x(3 + 5x)) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) ((3 * -8 + 5x * -8) + x(3 + 5x)) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) ((-24 + -40x) + x(3 + 5x)) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) (-24 + -40x + (3 * x + 5x * x)) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) (-24 + -40x + (3x + 5x2)) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) Combine like terms: -40x + 3x = -37x (-24 + -37x + 5x2) + (x + 7)(3x + 6) = (3x + 6)(5x + 3) Reorder the terms: -24 + -37x + 5x2 + (7 + x)(3x + 6) = (3x + 6)(5x + 3) Reorder the terms: -24 + -37x + 5x2 + (7 + x)(6 + 3x) = (3x + 6)(5x + 3) Multiply (7 + x) * (6 + 3x) -24 + -37x + 5x2 + (7(6 + 3x) + x(6 + 3x)) = (3x + 6)(5x + 3) -24 + -37x + 5x2 + ((6 * 7 + 3x * 7) + x(6 + 3x)) = (3x + 6)(5x + 3) -24 + -37x + 5x2 + ((42 + 21x) + x(6 + 3x)) = (3x + 6)(5x + 3) -24 + -37x + 5x2 + (42 + 21x + (6 * x + 3x * x)) = (3x + 6)(5x + 3) -24 + -37x + 5x2 + (42 + 21x + (6x + 3x2)) = (3x + 6)(5x + 3) Combine like terms: 21x + 6x = 27x -24 + -37x + 5x2 + (42 + 27x + 3x2) = (3x + 6)(5x + 3) Reorder the terms: -24 + 42 + -37x + 27x + 5x2 + 3x2 = (3x + 6)(5x + 3) Combine like terms: -24 + 42 = 18 18 + -37x + 27x + 5x2 + 3x2 = (3x + 6)(5x + 3) Combine like terms: -37x + 27x = -10x 18 + -10x + 5x2 + 3x2 = (3x + 6)(5x + 3) Combine like terms: 5x2 + 3x2 = 8x2 18 + -10x + 8x2 = (3x + 6)(5x + 3) Reorder the terms: 18 + -10x + 8x2 = (6 + 3x)(5x + 3) Reorder the terms: 18 + -10x + 8x2 = (6 + 3x)(3 + 5x) Multiply (6 + 3x) * (3 + 5x) 18 + -10x + 8x2 = (6(3 + 5x) + 3x * (3 + 5x)) 18 + -10x + 8x2 = ((3 * 6 + 5x * 6) + 3x * (3 + 5x)) 18 + -10x + 8x2 = ((18 + 30x) + 3x * (3 + 5x)) 18 + -10x + 8x2 = (18 + 30x + (3 * 3x + 5x * 3x)) 18 + -10x + 8x2 = (18 + 30x + (9x + 15x2)) Combine like terms: 30x + 9x = 39x 18 + -10x + 8x2 = (18 + 39x + 15x2) Add '-18' to each side of the equation. 18 + -10x + -18 + 8x2 = 18 + 39x + -18 + 15x2 Reorder the terms: 18 + -18 + -10x + 8x2 = 18 + 39x + -18 + 15x2 Combine like terms: 18 + -18 = 0 0 + -10x + 8x2 = 18 + 39x + -18 + 15x2 -10x + 8x2 = 18 + 39x + -18 + 15x2 Reorder the terms: -10x + 8x2 = 18 + -18 + 39x + 15x2 Combine like terms: 18 + -18 = 0 -10x + 8x2 = 0 + 39x + 15x2 -10x + 8x2 = 39x + 15x2 Solving -10x + 8x2 = 39x + 15x2 Solving for variable 'x'. Reorder the terms: -10x + -39x + 8x2 + -15x2 = 39x + 15x2 + -39x + -15x2 Combine like terms: -10x + -39x = -49x -49x + 8x2 + -15x2 = 39x + 15x2 + -39x + -15x2 Combine like terms: 8x2 + -15x2 = -7x2 -49x + -7x2 = 39x + 15x2 + -39x + -15x2 Reorder the terms: -49x + -7x2 = 39x + -39x + 15x2 + -15x2 Combine like terms: 39x + -39x = 0 -49x + -7x2 = 0 + 15x2 + -15x2 -49x + -7x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -49x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-7x'. -7x(7 + x) = 0 Ignore the factor -7.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {0, -7}
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