x^2-8ax=9a^2

Solution for x^2-8ax=9a^2 equation:

Simplifying
x2 + -8ax = 9a2

Reorder the terms:
-8ax + x2 = 9a2

Solving
-8ax + x2 = 9a2

Solving for variable 'a'.

Reorder the terms:
-8ax + -9a2 + x2 = 9a2 + -9a2

Combine like terms: 9a2 + -9a2 = 0
-8ax + -9a2 + x2 = 0

Factor a trinomial.
(-1a + -1x)(9a + -1x) = 0

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

Simplifying
-1a + -1x = 0

Solving
-1a + -1x = 0

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

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

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

Divide each side by '-1'.
a = -1x

Simplifying
a = -1x
Subproblem 2
Set the factor '(9a + -1x)' equal to zero and attempt to solve:

Simplifying
9a + -1x = 0

Solving
9a + -1x = 0

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

Add 'x' to each side of the equation.
9a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
9a + 0 = 0 + x
9a = 0 + x
Remove the zero:
9a = x

Divide each side by '9'.
a = 0.1111111111x

Simplifying
a = 0.1111111111x
Solution
a = {-1x, 0.1111111111x}