(4x+12y)(5x-y)=0

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Solution for (4x+12y)(5x-y)=0 equation: 


Simplifying
(4x + 12y)(5x + -1y) = 0

Multiply (4x + 12y) * (5x + -1y)
(4x * (5x + -1y) + 12y * (5x + -1y)) = 0
((5x * 4x + -1y * 4x) + 12y * (5x + -1y)) = 0

Reorder the terms:
((-4xy + 20x2) + 12y * (5x + -1y)) = 0
((-4xy + 20x2) + 12y * (5x + -1y)) = 0
(-4xy + 20x2 + (5x * 12y + -1y * 12y)) = 0
(-4xy + 20x2 + (60xy + -12y2)) = 0

Reorder the terms:
(-4xy + 60xy + 20x2 + -12y2) = 0

Combine like terms: -4xy + 60xy = 56xy
(56xy + 20x2 + -12y2) = 0

Solving
56xy + 20x2 + -12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(14xy + 5x2 + -3y2) = 0

Factor a trinomial.
4((5x + -1y)(x + 3y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5x + -1y)' equal to zero and attempt to solve:

Simplifying
5x + -1y = 0

Solving
5x + -1y = 0

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

Add 'y' to each side of the equation.
5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
5x + 0 = 0 + y
5x = 0 + y
Remove the zero:
5x = y

Divide each side by '5'.
x = 0.2y

Simplifying
x = 0.2y

Subproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

Add '-3y' to each side of the equation.
x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
x + 0 = 0 + -3y
x = 0 + -3y
Remove the zero:
x = -3y

Simplifying
x = -3y
Solution
x = {0.2y, -3y}

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