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

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


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

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

Reorder the terms:
((12xy + 10x2) + y(5x + 6y)) = 0
((12xy + 10x2) + y(5x + 6y)) = 0
(12xy + 10x2 + (5x * y + 6y * y)) = 0
(12xy + 10x2 + (5xy + 6y2)) = 0

Reorder the terms:
(12xy + 5xy + 10x2 + 6y2) = 0

Combine like terms: 12xy + 5xy = 17xy
(17xy + 10x2 + 6y2) = 0

Solving
17xy + 10x2 + 6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + y)(5x + 6y) = 0


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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y

Subproblem 2
Set the factor '(5x + 6y)' equal to zero and attempt to solve:

Simplifying
5x + 6y = 0

Solving
5x + 6y = 0

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

Add '-6y' to each side of the equation.
5x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
5x + 0 = 0 + -6y
5x = 0 + -6y
Remove the zero:
5x = -6y

Divide each side by '5'.
x = -1.2y

Simplifying
x = -1.2y
Solution
x = {-0.5y, -1.2y}

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