(56x-4y)45(61x+y)=0

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Solution for (56x-4y)45(61x+y)=0 equation: 


Simplifying
(56x + -4y) * 45(61x + y) = 0

Reorder the terms for easier multiplication:
45(56x + -4y)(61x + y) = 0

Multiply (56x + -4y) * (61x + y)
45(56x * (61x + y) + -4y * (61x + y)) = 0
45((61x * 56x + y * 56x) + -4y * (61x + y)) = 0

Reorder the terms:
45((56xy + 3416x2) + -4y * (61x + y)) = 0
45((56xy + 3416x2) + -4y * (61x + y)) = 0
45(56xy + 3416x2 + (61x * -4y + y * -4y)) = 0
45(56xy + 3416x2 + (-244xy + -4y2)) = 0

Reorder the terms:
45(56xy + -244xy + 3416x2 + -4y2) = 0

Combine like terms: 56xy + -244xy = -188xy
45(-188xy + 3416x2 + -4y2) = 0
(-188xy * 45 + 3416x2 * 45 + -4y2 * 45) = 0
(-8460xy + 153720x2 + -180y2) = 0

Solving
-8460xy + 153720x2 + -180y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '180'.
180(-47xy + 854x2 + -1y2) = 0

Factor a trinomial.
180((14x + -1y)(61x + y)) = 0

Ignore the factor 180.

Subproblem 1
Set the factor '(14x + -1y)' equal to zero and attempt to solve:

Simplifying
14x + -1y = 0

Solving
14x + -1y = 0

Move all terms containing x to the left, all other terms to the right.

Add 'y' to each side of the equation.
14x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
14x + 0 = 0 + y
14x = 0 + y
Remove the zero:
14x = y

Divide each side by '14'.
x = 0.07142857143y

Simplifying
x = 0.07142857143y

Subproblem 2
Set the factor '(61x + y)' equal to zero and attempt to solve:

Simplifying
61x + y = 0

Solving
61x + y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1y' to each side of the equation.
61x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
61x + 0 = 0 + -1y
61x = 0 + -1y
Remove the zero:
61x = -1y

Divide each side by '61'.
x = -0.01639344262y

Simplifying
x = -0.01639344262y
Solution
x = {0.07142857143y, -0.01639344262y}

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