b(2y+a)=a(2y+b)

Solution for b(2y+a)=a(2y+b) equation:

Simplifying
b(2y + a) = a(2y + b)

Reorder the terms:
b(a + 2y) = a(2y + b)
(a * b + 2y * b) = a(2y + b)
(ab + 2by) = a(2y + b)

Reorder the terms:
ab + 2by = a(b + 2y)
ab + 2by = (b * a + 2y * a)
ab + 2by = (ab + 2ay)

Add '-1ab' to each side of the equation.
ab + -1ab + 2by = ab + -1ab + 2ay

Combine like terms: ab + -1ab = 0
0 + 2by = ab + -1ab + 2ay
2by = ab + -1ab + 2ay

Combine like terms: ab + -1ab = 0
2by = 0 + 2ay
2by = 2ay

Solving
2by = 2ay

Solving for variable 'b'.

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

Divide each side by '2y'.
b = a

Simplifying
b = a