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Simplifying 2(x + -1c) * 4(x + -1b) = 2(x + c)(4x + -1b) Reorder the terms: 2(-1c + x) * 4(x + -1b) = 2(x + c)(4x + -1b) Reorder the terms: 2(-1c + x) * 4(-1b + x) = 2(x + c)(4x + -1b) Reorder the terms for easier multiplication: 2 * 4(-1c + x)(-1b + x) = 2(x + c)(4x + -1b) Multiply 2 * 4 8(-1c + x)(-1b + x) = 2(x + c)(4x + -1b) Multiply (-1c + x) * (-1b + x) 8(-1c * (-1b + x) + x(-1b + x)) = 2(x + c)(4x + -1b) 8((-1b * -1c + x * -1c) + x(-1b + x)) = 2(x + c)(4x + -1b) 8((1bc + -1cx) + x(-1b + x)) = 2(x + c)(4x + -1b) 8(1bc + -1cx + (-1b * x + x * x)) = 2(x + c)(4x + -1b) 8(1bc + -1cx + (-1bx + x2)) = 2(x + c)(4x + -1b) Reorder the terms: 8(1bc + -1bx + -1cx + x2) = 2(x + c)(4x + -1b) 8(1bc + -1bx + -1cx + x2) = 2(x + c)(4x + -1b) (1bc * 8 + -1bx * 8 + -1cx * 8 + x2 * 8) = 2(x + c)(4x + -1b) (8bc + -8bx + -8cx + 8x2) = 2(x + c)(4x + -1b) Reorder the terms: 8bc + -8bx + -8cx + 8x2 = 2(c + x)(4x + -1b) Reorder the terms: 8bc + -8bx + -8cx + 8x2 = 2(c + x)(-1b + 4x) Multiply (c + x) * (-1b + 4x) 8bc + -8bx + -8cx + 8x2 = 2(c(-1b + 4x) + x(-1b + 4x)) 8bc + -8bx + -8cx + 8x2 = 2((-1b * c + 4x * c) + x(-1b + 4x)) 8bc + -8bx + -8cx + 8x2 = 2((-1bc + 4cx) + x(-1b + 4x)) 8bc + -8bx + -8cx + 8x2 = 2(-1bc + 4cx + (-1b * x + 4x * x)) 8bc + -8bx + -8cx + 8x2 = 2(-1bc + 4cx + (-1bx + 4x2)) Reorder the terms: 8bc + -8bx + -8cx + 8x2 = 2(-1bc + -1bx + 4cx + 4x2) 8bc + -8bx + -8cx + 8x2 = 2(-1bc + -1bx + 4cx + 4x2) 8bc + -8bx + -8cx + 8x2 = (-1bc * 2 + -1bx * 2 + 4cx * 2 + 4x2 * 2) 8bc + -8bx + -8cx + 8x2 = (-2bc + -2bx + 8cx + 8x2) Add '-8x2' to each side of the equation. 8bc + -8bx + -8cx + 8x2 + -8x2 = -2bc + -2bx + 8cx + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 8bc + -8bx + -8cx + 0 = -2bc + -2bx + 8cx + 8x2 + -8x2 8bc + -8bx + -8cx = -2bc + -2bx + 8cx + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 8bc + -8bx + -8cx = -2bc + -2bx + 8cx + 0 8bc + -8bx + -8cx = -2bc + -2bx + 8cx Solving 8bc + -8bx + -8cx = -2bc + -2bx + 8cx Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2bc' to each side of the equation. 8bc + -8bx + 2bc + -8cx = -2bc + -2bx + 2bc + 8cx Reorder the terms: 8bc + 2bc + -8bx + -8cx = -2bc + -2bx + 2bc + 8cx Combine like terms: 8bc + 2bc = 10bc 10bc + -8bx + -8cx = -2bc + -2bx + 2bc + 8cx Reorder the terms: 10bc + -8bx + -8cx = -2bc + 2bc + -2bx + 8cx Combine like terms: -2bc + 2bc = 0 10bc + -8bx + -8cx = 0 + -2bx + 8cx 10bc + -8bx + -8cx = -2bx + 8cx Add '2bx' to each side of the equation. 10bc + -8bx + 2bx + -8cx = -2bx + 2bx + 8cx Combine like terms: -8bx + 2bx = -6bx 10bc + -6bx + -8cx = -2bx + 2bx + 8cx Combine like terms: -2bx + 2bx = 0 10bc + -6bx + -8cx = 0 + 8cx 10bc + -6bx + -8cx = 8cx Add '8cx' to each side of the equation. 10bc + -6bx + -8cx + 8cx = 8cx + 8cx Combine like terms: -8cx + 8cx = 0 10bc + -6bx + 0 = 8cx + 8cx 10bc + -6bx = 8cx + 8cx Combine like terms: 8cx + 8cx = 16cx 10bc + -6bx = 16cx Combine like terms: 16cx + -16cx = 0 10bc + -6bx + -16cx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5bc + -3bx + -8cx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5bc + -3bx + -8cx)' equal to zero and attempt to solve: Simplifying 5bc + -3bx + -8cx = 0 Solving 5bc + -3bx + -8cx = 0 Move all terms containing b to the left, all other terms to the right. Add '8cx' to each side of the equation. 5bc + -3bx + -8cx + 8cx = 0 + 8cx Combine like terms: -8cx + 8cx = 0 5bc + -3bx + 0 = 0 + 8cx 5bc + -3bx = 0 + 8cx Remove the zero: 5bc + -3bx = 8cx 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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