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Simplifying 3x(6x + -10y)(37x + -67b) = 0 Reorder the terms: 3x(6x + -10y)(-67b + 37x) = 0 Multiply (6x + -10y) * (-67b + 37x) 3x(6x * (-67b + 37x) + -10y * (-67b + 37x)) = 0 3x((-67b * 6x + 37x * 6x) + -10y * (-67b + 37x)) = 0 3x((-402bx + 222x2) + -10y * (-67b + 37x)) = 0 3x(-402bx + 222x2 + (-67b * -10y + 37x * -10y)) = 0 3x(-402bx + 222x2 + (670by + -370xy)) = 0 Reorder the terms: 3x(-402bx + 670by + -370xy + 222x2) = 0 3x(-402bx + 670by + -370xy + 222x2) = 0 (-402bx * 3x + 670by * 3x + -370xy * 3x + 222x2 * 3x) = 0 Reorder the terms: (2010bxy + -1206bx2 + -1110x2y + 666x3) = 0 (2010bxy + -1206bx2 + -1110x2y + 666x3) = 0 Solving 2010bxy + -1206bx2 + -1110x2y + 666x3 = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1110x2y' to each side of the equation. 2010bxy + -1206bx2 + -1110x2y + 1110x2y + 666x3 = 0 + 1110x2y Combine like terms: -1110x2y + 1110x2y = 0 2010bxy + -1206bx2 + 0 + 666x3 = 0 + 1110x2y 2010bxy + -1206bx2 + 666x3 = 0 + 1110x2y Remove the zero: 2010bxy + -1206bx2 + 666x3 = 1110x2y Add '-666x3' to each side of the equation. 2010bxy + -1206bx2 + 666x3 + -666x3 = 1110x2y + -666x3 Combine like terms: 666x3 + -666x3 = 0 2010bxy + -1206bx2 + 0 = 1110x2y + -666x3 2010bxy + -1206bx2 = 1110x2y + -666x3 Reorder the terms: 2010bxy + -1206bx2 + -1110x2y + 666x3 = 1110x2y + -1110x2y + -666x3 + 666x3 Combine like terms: 1110x2y + -1110x2y = 0 2010bxy + -1206bx2 + -1110x2y + 666x3 = 0 + -666x3 + 666x3 2010bxy + -1206bx2 + -1110x2y + 666x3 = -666x3 + 666x3 Combine like terms: -666x3 + 666x3 = 0 2010bxy + -1206bx2 + -1110x2y + 666x3 = 0 Factor out the Greatest Common Factor (GCF), '6x'. 6x(335by + -201bx + -185xy + 111x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing b to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(335by + -201bx + -185xy + 111x2)' equal to zero and attempt to solve: Simplifying 335by + -201bx + -185xy + 111x2 = 0 Reorder the terms: -201bx + 335by + -185xy + 111x2 = 0 Solving -201bx + 335by + -185xy + 111x2 = 0 Move all terms containing b to the left, all other terms to the right. Add '185xy' to each side of the equation. -201bx + 335by + -185xy + 185xy + 111x2 = 0 + 185xy Combine like terms: -185xy + 185xy = 0 -201bx + 335by + 0 + 111x2 = 0 + 185xy -201bx + 335by + 111x2 = 0 + 185xy Remove the zero: -201bx + 335by + 111x2 = 185xy Add '-111x2' to each side of the equation. -201bx + 335by + 111x2 + -111x2 = 185xy + -111x2 Combine like terms: 111x2 + -111x2 = 0 -201bx + 335by + 0 = 185xy + -111x2 -201bx + 335by = 185xy + -111x2 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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