(2y+w)(y+5w)=

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Solution for (2y+w)(y+5w)= equation: 


Simplifying
(2y + w)(y + 5w) = 0

Reorder the terms:
(w + 2y)(y + 5w) = 0

Reorder the terms:
(w + 2y)(5w + y) = 0

Multiply (w + 2y) * (5w + y)
(w(5w + y) + 2y * (5w + y)) = 0
((5w * w + y * w) + 2y * (5w + y)) = 0

Reorder the terms:
((wy + 5w2) + 2y * (5w + y)) = 0
((wy + 5w2) + 2y * (5w + y)) = 0
(wy + 5w2 + (5w * 2y + y * 2y)) = 0
(wy + 5w2 + (10wy + 2y2)) = 0

Reorder the terms:
(wy + 10wy + 5w2 + 2y2) = 0

Combine like terms: wy + 10wy = 11wy
(11wy + 5w2 + 2y2) = 0

Solving
11wy + 5w2 + 2y2 = 0

Solving for variable 'w'.

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


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

Simplifying
5w + y = 0

Solving
5w + y = 0

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

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

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

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

Simplifying
w = -0.2y

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

Simplifying
w + 2y = 0

Solving
w + 2y = 0

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

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

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

Simplifying
w = -2y
Solution
w = {-0.2y, -2y}

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