=6a^2y-2abx-3aby+4a^2x

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Solution for =6a^2y-2abx-3aby+4a^2x equation:


Simplifying
0 = 6a2y + -2abx + -3aby + 4a2x

Reorder the terms:
0 = -2abx + -3aby + 4a2x + 6a2y

Solving
0 = -2abx + -3aby + 4a2x + 6a2y

Solving for variable 'a'.
Remove the zero:
2abx + 3aby + -4a2x + -6a2y = -2abx + -3aby + 4a2x + 6a2y + 2abx + 3aby + -4a2x + -6a2y

Reorder the terms:
2abx + 3aby + -4a2x + -6a2y = -2abx + 2abx + -3aby + 3aby + 4a2x + -4a2x + 6a2y + -6a2y

Combine like terms: -2abx + 2abx = 0
2abx + 3aby + -4a2x + -6a2y = 0 + -3aby + 3aby + 4a2x + -4a2x + 6a2y + -6a2y
2abx + 3aby + -4a2x + -6a2y = -3aby + 3aby + 4a2x + -4a2x + 6a2y + -6a2y

Combine like terms: -3aby + 3aby = 0
2abx + 3aby + -4a2x + -6a2y = 0 + 4a2x + -4a2x + 6a2y + -6a2y
2abx + 3aby + -4a2x + -6a2y = 4a2x + -4a2x + 6a2y + -6a2y

Combine like terms: 4a2x + -4a2x = 0
2abx + 3aby + -4a2x + -6a2y = 0 + 6a2y + -6a2y
2abx + 3aby + -4a2x + -6a2y = 6a2y + -6a2y

Combine like terms: 6a2y + -6a2y = 0
2abx + 3aby + -4a2x + -6a2y = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(2bx + 3by + -4ax + -6ay) = 0

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 = 0

Subproblem 2

Set the factor '(2bx + 3by + -4ax + -6ay)' equal to zero and attempt to solve: Simplifying 2bx + 3by + -4ax + -6ay = 0 Reorder the terms: -4ax + -6ay + 2bx + 3by = 0 Solving -4ax + -6ay + 2bx + 3by = 0 Move all terms containing a to the left, all other terms to the right. Add '-2bx' to each side of the equation. -4ax + -6ay + 2bx + -2bx + 3by = 0 + -2bx Combine like terms: 2bx + -2bx = 0 -4ax + -6ay + 0 + 3by = 0 + -2bx -4ax + -6ay + 3by = 0 + -2bx Remove the zero: -4ax + -6ay + 3by = -2bx Add '-3by' to each side of the equation. -4ax + -6ay + 3by + -3by = -2bx + -3by Combine like terms: 3by + -3by = 0 -4ax + -6ay + 0 = -2bx + -3by -4ax + -6ay = -2bx + -3by 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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