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Simplifying (x + -8)(a + b) + (x + -8)(a + 7b) = 0 Reorder the terms: (-8 + x)(a + b) + (x + -8)(a + 7b) = 0 Multiply (-8 + x) * (a + b) (-8(a + b) + x(a + b)) + (x + -8)(a + 7b) = 0 ((a * -8 + b * -8) + x(a + b)) + (x + -8)(a + 7b) = 0 ((-8a + -8b) + x(a + b)) + (x + -8)(a + 7b) = 0 (-8a + -8b + (a * x + b * x)) + (x + -8)(a + 7b) = 0 (-8a + -8b + (ax + bx)) + (x + -8)(a + 7b) = 0 Reorder the terms: (-8a + ax + -8b + bx) + (x + -8)(a + 7b) = 0 (-8a + ax + -8b + bx) + (x + -8)(a + 7b) = 0 Reorder the terms: -8a + ax + -8b + bx + (-8 + x)(a + 7b) = 0 Multiply (-8 + x) * (a + 7b) -8a + ax + -8b + bx + (-8(a + 7b) + x(a + 7b)) = 0 -8a + ax + -8b + bx + ((a * -8 + 7b * -8) + x(a + 7b)) = 0 -8a + ax + -8b + bx + ((-8a + -56b) + x(a + 7b)) = 0 -8a + ax + -8b + bx + (-8a + -56b + (a * x + 7b * x)) = 0 -8a + ax + -8b + bx + (-8a + -56b + (ax + 7bx)) = 0 Reorder the terms: -8a + ax + -8b + bx + (-8a + ax + -56b + 7bx) = 0 -8a + ax + -8b + bx + (-8a + ax + -56b + 7bx) = 0 Reorder the terms: -8a + -8a + ax + ax + -8b + -56b + bx + 7bx = 0 Combine like terms: -8a + -8a = -16a -16a + ax + ax + -8b + -56b + bx + 7bx = 0 Combine like terms: ax + ax = 2ax -16a + 2ax + -8b + -56b + bx + 7bx = 0 Combine like terms: -8b + -56b = -64b -16a + 2ax + -64b + bx + 7bx = 0 Combine like terms: bx + 7bx = 8bx -16a + 2ax + -64b + 8bx = 0 Solving -16a + 2ax + -64b + 8bx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '64b' to each side of the equation. -16a + 2ax + -64b + 64b + 8bx = 0 + 64b Combine like terms: -64b + 64b = 0 -16a + 2ax + 0 + 8bx = 0 + 64b -16a + 2ax + 8bx = 0 + 64b Remove the zero: -16a + 2ax + 8bx = 64b Add '-8bx' to each side of the equation. -16a + 2ax + 8bx + -8bx = 64b + -8bx Combine like terms: 8bx + -8bx = 0 -16a + 2ax + 0 = 64b + -8bx -16a + 2ax = 64b + -8bx Reorder the terms: -16a + 2ax + -64b + 8bx = 64b + -64b + -8bx + 8bx Combine like terms: 64b + -64b = 0 -16a + 2ax + -64b + 8bx = 0 + -8bx + 8bx -16a + 2ax + -64b + 8bx = -8bx + 8bx Combine like terms: -8bx + 8bx = 0 -16a + 2ax + -64b + 8bx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8a + ax + -32b + 4bx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8a + ax + -32b + 4bx)' equal to zero and attempt to solve: Simplifying -8a + ax + -32b + 4bx = 0 Solving -8a + ax + -32b + 4bx = 0 Move all terms containing a to the left, all other terms to the right. Add '32b' to each side of the equation. -8a + ax + -32b + 32b + 4bx = 0 + 32b Combine like terms: -32b + 32b = 0 -8a + ax + 0 + 4bx = 0 + 32b -8a + ax + 4bx = 0 + 32b Remove the zero: -8a + ax + 4bx = 32b Add '-4bx' to each side of the equation. -8a + ax + 4bx + -4bx = 32b + -4bx Combine like terms: 4bx + -4bx = 0 -8a + ax + 0 = 32b + -4bx -8a + ax = 32b + -4bx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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