a^2+9ab+b^2=7ab

Solution for a^2+9ab+b^2=7ab equation:

Simplifying
a2 + 9ab + b2 = 7ab

Reorder the terms:
9ab + a2 + b2 = 7ab

Solving
9ab + a2 + b2 = 7ab

Solving for variable 'a'.

Reorder the terms:
9ab + -7ab + a2 + b2 = 7ab + -7ab

Combine like terms: 9ab + -7ab = 2ab
2ab + a2 + b2 = 7ab + -7ab

Combine like terms: 7ab + -7ab = 0
2ab + a2 + b2 = 0

Factor a trinomial.
(a + b)(a + b) = 0

Subproblem 1
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b
Subproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b
Solution
a = {-1b, -1b}