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Simplifying 4(a + b + 1)(b + c + -8) = 0 Reorder the terms: 4(1 + a + b)(b + c + -8) = 0 Reorder the terms: 4(1 + a + b)(-8 + b + c) = 0 Multiply (1 + a + b) * (-8 + b + c) 4(1(-8 + b + c) + a(-8 + b + c) + b(-8 + b + c)) = 0 4((-8 * 1 + b * 1 + c * 1) + a(-8 + b + c) + b(-8 + b + c)) = 0 4((-8 + 1b + 1c) + a(-8 + b + c) + b(-8 + b + c)) = 0 4(-8 + 1b + 1c + (-8 * a + b * a + c * a) + b(-8 + b + c)) = 0 4(-8 + 1b + 1c + (-8a + ab + ac) + b(-8 + b + c)) = 0 4(-8 + 1b + 1c + -8a + ab + ac + (-8 * b + b * b + c * b)) = 0 Reorder the terms: 4(-8 + 1b + 1c + -8a + ab + ac + (-8b + bc + b2)) = 0 4(-8 + 1b + 1c + -8a + ab + ac + (-8b + bc + b2)) = 0 Reorder the terms: 4(-8 + -8a + ab + ac + 1b + -8b + bc + b2 + 1c) = 0 Combine like terms: 1b + -8b = -7b 4(-8 + -8a + ab + ac + -7b + bc + b2 + 1c) = 0 (-8 * 4 + -8a * 4 + ab * 4 + ac * 4 + -7b * 4 + bc * 4 + b2 * 4 + 1c * 4) = 0 (-32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c) = 0 Solving -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '32' to each side of the equation. -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 32 + 4c = 0 + 32 Reorder the terms: -32 + 32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 + 32 -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 + 32 Combine like terms: 0 + 32 = 32 -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 32 Add '28b' to each side of the equation. -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 28b + 4c = 32 + 28b Reorder the terms: -32a + 4ab + 4ac + -28b + 28b + 4bc + 4b2 + 4c = 32 + 28b Combine like terms: -28b + 28b = 0 -32a + 4ab + 4ac + 0 + 4bc + 4b2 + 4c = 32 + 28b -32a + 4ab + 4ac + 4bc + 4b2 + 4c = 32 + 28b Add '-4bc' to each side of the equation. -32a + 4ab + 4ac + 4bc + 4b2 + -4bc + 4c = 32 + 28b + -4bc Reorder the terms: -32a + 4ab + 4ac + 4bc + -4bc + 4b2 + 4c = 32 + 28b + -4bc Combine like terms: 4bc + -4bc = 0 -32a + 4ab + 4ac + 0 + 4b2 + 4c = 32 + 28b + -4bc -32a + 4ab + 4ac + 4b2 + 4c = 32 + 28b + -4bc Add '-4b2' to each side of the equation. -32a + 4ab + 4ac + 4b2 + -4b2 + 4c = 32 + 28b + -4bc + -4b2 Combine like terms: 4b2 + -4b2 = 0 -32a + 4ab + 4ac + 0 + 4c = 32 + 28b + -4bc + -4b2 -32a + 4ab + 4ac + 4c = 32 + 28b + -4bc + -4b2 Add '-4c' to each side of the equation. -32a + 4ab + 4ac + 4c + -4c = 32 + 28b + -4bc + -4b2 + -4c Combine like terms: 4c + -4c = 0 -32a + 4ab + 4ac + 0 = 32 + 28b + -4bc + -4b2 + -4c -32a + 4ab + 4ac = 32 + 28b + -4bc + -4b2 + -4c Reorder the terms: -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 32 + 28b + -4bc + -4b2 + -4c + -32 + -28b + 4bc + 4b2 + 4c Reorder the terms: -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 32 + -32 + 28b + -28b + -4bc + 4bc + -4b2 + 4b2 + -4c + 4c Combine like terms: 32 + -32 = 0 -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 + 28b + -28b + -4bc + 4bc + -4b2 + 4b2 + -4c + 4c -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 28b + -28b + -4bc + 4bc + -4b2 + 4b2 + -4c + 4c Combine like terms: 28b + -28b = 0 -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 + -4bc + 4bc + -4b2 + 4b2 + -4c + 4c -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = -4bc + 4bc + -4b2 + 4b2 + -4c + 4c Combine like terms: -4bc + 4bc = 0 -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 + -4b2 + 4b2 + -4c + 4c -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = -4b2 + 4b2 + -4c + 4c Combine like terms: -4b2 + 4b2 = 0 -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 + -4c + 4c -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = -4c + 4c Combine like terms: -4c + 4c = 0 -32 + -32a + 4ab + 4ac + -28b + 4bc + 4b2 + 4c = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + -8a + ab + ac + -7b + bc + b2 + c) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -8a + ab + ac + -7b + bc + b2 + c)' equal to zero and attempt to solve: Simplifying -8 + -8a + ab + ac + -7b + bc + b2 + c = 0 Solving -8 + -8a + ab + ac + -7b + bc + b2 + c = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + -8a + ab + ac + -7b + bc + b2 + 8 + c = 0 + 8 Reorder the terms: -8 + 8 + -8a + ab + ac + -7b + bc + b2 + c = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -8a + ab + ac + -7b + bc + b2 + c = 0 + 8 -8a + ab + ac + -7b + bc + b2 + c = 0 + 8 Combine like terms: 0 + 8 = 8 -8a + ab + ac + -7b + bc + b2 + c = 8 Add '7b' to each side of the equation. -8a + ab + ac + -7b + bc + b2 + 7b + c = 8 + 7b Reorder the terms: -8a + ab + ac + -7b + 7b + bc + b2 + c = 8 + 7b Combine like terms: -7b + 7b = 0 -8a + ab + ac + 0 + bc + b2 + c = 8 + 7b -8a + ab + ac + bc + b2 + c = 8 + 7b Add '-1bc' to each side of the equation. -8a + ab + ac + bc + b2 + -1bc + c = 8 + 7b + -1bc Reorder the terms: -8a + ab + ac + bc + -1bc + b2 + c = 8 + 7b + -1bc Combine like terms: bc + -1bc = 0 -8a + ab + ac + 0 + b2 + c = 8 + 7b + -1bc -8a + ab + ac + b2 + c = 8 + 7b + -1bc Add '-1b2' to each side of the equation. -8a + ab + ac + b2 + -1b2 + c = 8 + 7b + -1bc + -1b2 Combine like terms: b2 + -1b2 = 0 -8a + ab + ac + 0 + c = 8 + 7b + -1bc + -1b2 -8a + ab + ac + c = 8 + 7b + -1bc + -1b2 Add '-1c' to each side of the equation. -8a + ab + ac + c + -1c = 8 + 7b + -1bc + -1b2 + -1c Combine like terms: c + -1c = 0 -8a + ab + ac + 0 = 8 + 7b + -1bc + -1b2 + -1c -8a + ab + ac = 8 + 7b + -1bc + -1b2 + -1c 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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