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Simplifying 4ab(3x + -1y) + -6a(3x + -1y) = 0 (3x * 4ab + -1y * 4ab) + -6a(3x + -1y) = 0 (12abx + -4aby) + -6a(3x + -1y) = 0 12abx + -4aby + (3x * -6a + -1y * -6a) = 0 12abx + -4aby + (-18ax + 6ay) = 0 Solving 12abx + -4aby + -18ax + 6ay = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2a'. 2a(6bx + -2by + -9x + 3y) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(6bx + -2by + -9x + 3y)' equal to zero and attempt to solve: Simplifying 6bx + -2by + -9x + 3y = 0 Solving 6bx + -2by + -9x + 3y = 0 Move all terms containing a to the left, all other terms to the right. Add '-6bx' to each side of the equation. 6bx + -2by + -9x + -6bx + 3y = 0 + -6bx Reorder the terms: 6bx + -6bx + -2by + -9x + 3y = 0 + -6bx Combine like terms: 6bx + -6bx = 0 0 + -2by + -9x + 3y = 0 + -6bx -2by + -9x + 3y = 0 + -6bx Remove the zero: -2by + -9x + 3y = -6bx Add '2by' to each side of the equation. -2by + -9x + 2by + 3y = -6bx + 2by Reorder the terms: -2by + 2by + -9x + 3y = -6bx + 2by Combine like terms: -2by + 2by = 0 0 + -9x + 3y = -6bx + 2by -9x + 3y = -6bx + 2by Add '9x' to each side of the equation. -9x + 9x + 3y = -6bx + 2by + 9x Combine like terms: -9x + 9x = 0 0 + 3y = -6bx + 2by + 9x 3y = -6bx + 2by + 9x Add '-3y' to each side of the equation. 3y + -3y = -6bx + 2by + 9x + -3y Combine like terms: 3y + -3y = 0 0 = -6bx + 2by + 9x + -3y Simplifying 0 = -6bx + 2by + 9x + -3y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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