(-5x-y)(6x+2y)=

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Solution for (-5x-y)(6x+2y)= equation: 


Simplifying
(-5x + -1y)(6x + 2y) = 0

Multiply (-5x + -1y) * (6x + 2y)
(-5x * (6x + 2y) + -1y * (6x + 2y)) = 0
((6x * -5x + 2y * -5x) + -1y * (6x + 2y)) = 0

Reorder the terms:
((-10xy + -30x2) + -1y * (6x + 2y)) = 0
((-10xy + -30x2) + -1y * (6x + 2y)) = 0
(-10xy + -30x2 + (6x * -1y + 2y * -1y)) = 0
(-10xy + -30x2 + (-6xy + -2y2)) = 0

Reorder the terms:
(-10xy + -6xy + -30x2 + -2y2) = 0

Combine like terms: -10xy + -6xy = -16xy
(-16xy + -30x2 + -2y2) = 0

Solving
-16xy + -30x2 + -2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(8xy + 15x2 + y2) = 0

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

Ignore the factor -2.

Subproblem 1
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

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

Simplifying
3x + y = 0

Solving
3x + y = 0

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

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y
Solution
x = {-0.2y, -0.3333333333y}

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