(5x+y)(6x-4y)=

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Solution for (5x+y)(6x-4y)= equation: 


Simplifying
(5x + y)(6x + -4y) = 0

Multiply (5x + y) * (6x + -4y)
(5x * (6x + -4y) + y(6x + -4y)) = 0
((6x * 5x + -4y * 5x) + y(6x + -4y)) = 0

Reorder the terms:
((-20xy + 30x2) + y(6x + -4y)) = 0
((-20xy + 30x2) + y(6x + -4y)) = 0
(-20xy + 30x2 + (6x * y + -4y * y)) = 0
(-20xy + 30x2 + (6xy + -4y2)) = 0

Reorder the terms:
(-20xy + 6xy + 30x2 + -4y2) = 0

Combine like terms: -20xy + 6xy = -14xy
(-14xy + 30x2 + -4y2) = 0

Solving
-14xy + 30x2 + -4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7xy + 15x2 + -2y2) = 0

Factor a trinomial.
2((3x + -2y)(5x + y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve:

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

Subproblem 2
Set the factor '(5x + y)' equal to zero and attempt to solve:

Simplifying
5x + y = 0

Solving
5x + y = 0

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

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

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

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

Simplifying
x = -0.2y
Solution
x = {0.6666666667y, -0.2y}

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