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Simplifying (7x + 1) * by(7x + 5) = (3x + 1) * by(5x + 1) Reorder the terms: (1 + 7x) * by(7x + 5) = (3x + 1) * by(5x + 1) Reorder the terms: (1 + 7x) * by(5 + 7x) = (3x + 1) * by(5x + 1) Reorder the terms for easier multiplication: by(1 + 7x)(5 + 7x) = (3x + 1) * by(5x + 1) Multiply (1 + 7x) * (5 + 7x) by(1(5 + 7x) + 7x * (5 + 7x)) = (3x + 1) * by(5x + 1) by((5 * 1 + 7x * 1) + 7x * (5 + 7x)) = (3x + 1) * by(5x + 1) by((5 + 7x) + 7x * (5 + 7x)) = (3x + 1) * by(5x + 1) by(5 + 7x + (5 * 7x + 7x * 7x)) = (3x + 1) * by(5x + 1) by(5 + 7x + (35x + 49x2)) = (3x + 1) * by(5x + 1) Combine like terms: 7x + 35x = 42x by(5 + 42x + 49x2) = (3x + 1) * by(5x + 1) (5 * by + 42x * by + 49x2 * by) = (3x + 1) * by(5x + 1) Reorder the terms: (42bxy + 49bx2y + 5by) = (3x + 1) * by(5x + 1) (42bxy + 49bx2y + 5by) = (3x + 1) * by(5x + 1) Reorder the terms: 42bxy + 49bx2y + 5by = (1 + 3x) * by(5x + 1) Reorder the terms: 42bxy + 49bx2y + 5by = (1 + 3x) * by(1 + 5x) Reorder the terms for easier multiplication: 42bxy + 49bx2y + 5by = by(1 + 3x)(1 + 5x) Multiply (1 + 3x) * (1 + 5x) 42bxy + 49bx2y + 5by = by(1(1 + 5x) + 3x * (1 + 5x)) 42bxy + 49bx2y + 5by = by((1 * 1 + 5x * 1) + 3x * (1 + 5x)) 42bxy + 49bx2y + 5by = by((1 + 5x) + 3x * (1 + 5x)) 42bxy + 49bx2y + 5by = by(1 + 5x + (1 * 3x + 5x * 3x)) 42bxy + 49bx2y + 5by = by(1 + 5x + (3x + 15x2)) Combine like terms: 5x + 3x = 8x 42bxy + 49bx2y + 5by = by(1 + 8x + 15x2) 42bxy + 49bx2y + 5by = (1 * by + 8x * by + 15x2 * by) Reorder the terms: 42bxy + 49bx2y + 5by = (8bxy + 15bx2y + 1by) 42bxy + 49bx2y + 5by = (8bxy + 15bx2y + 1by) Solving 42bxy + 49bx2y + 5by = 8bxy + 15bx2y + 1by Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8bxy' to each side of the equation. 42bxy + 49bx2y + -8bxy + 5by = 8bxy + 15bx2y + -8bxy + 1by Reorder the terms: 42bxy + -8bxy + 49bx2y + 5by = 8bxy + 15bx2y + -8bxy + 1by Combine like terms: 42bxy + -8bxy = 34bxy 34bxy + 49bx2y + 5by = 8bxy + 15bx2y + -8bxy + 1by Reorder the terms: 34bxy + 49bx2y + 5by = 8bxy + -8bxy + 15bx2y + 1by Combine like terms: 8bxy + -8bxy = 0 34bxy + 49bx2y + 5by = 0 + 15bx2y + 1by 34bxy + 49bx2y + 5by = 15bx2y + 1by Add '-15bx2y' to each side of the equation. 34bxy + 49bx2y + -15bx2y + 5by = 15bx2y + -15bx2y + 1by Combine like terms: 49bx2y + -15bx2y = 34bx2y 34bxy + 34bx2y + 5by = 15bx2y + -15bx2y + 1by Combine like terms: 15bx2y + -15bx2y = 0 34bxy + 34bx2y + 5by = 0 + 1by 34bxy + 34bx2y + 5by = 1by Add '-1by' to each side of the equation. 34bxy + 34bx2y + 5by + -1by = 1by + -1by Combine like terms: 5by + -1by = 4by 34bxy + 34bx2y + 4by = 1by + -1by Combine like terms: 1by + -1by = 0 34bxy + 34bx2y + 4by = 0 Factor out the Greatest Common Factor (GCF), '2by'. 2by(17x + 17x2 + 2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'by' equal to zero and attempt to solve: Simplifying by = 0 Solving by = 0 Move all terms containing b to the left, all other terms to the right. Simplifying by = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(17x + 17x2 + 2)' equal to zero and attempt to solve: Simplifying 17x + 17x2 + 2 = 0 Reorder the terms: 2 + 17x + 17x2 = 0 Solving 2 + 17x + 17x2 = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 17x + -2 + 17x2 = 0 + -2 Reorder the terms: 2 + -2 + 17x + 17x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 17x + 17x2 = 0 + -2 17x + 17x2 = 0 + -2 Combine like terms: 0 + -2 = -2 17x + 17x2 = -2 Add '-17x' to each side of the equation. 17x + -17x + 17x2 = -2 + -17x Combine like terms: 17x + -17x = 0 0 + 17x2 = -2 + -17x 17x2 = -2 + -17x Add '-17x2' to each side of the equation. 17x2 + -17x2 = -2 + -17x + -17x2 Combine like terms: 17x2 + -17x2 = 0 0 = -2 + -17x + -17x2 Simplifying 0 = -2 + -17x + -17x2 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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