72a^2-27ab-45b^2=

Solution for 72a^2-27ab-45b^2= equation:

Simplifying
72a2 + -27ab + -45b2 = 0

Reorder the terms:
-27ab + 72a2 + -45b2 = 0

Solving
-27ab + 72a2 + -45b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-3ab + 8a2 + -5b2) = 0

Factor a trinomial.
9((a + -1b)(8a + 5b)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(a + -1b)' equal to zero and attempt to solve:

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

Simplifying
a = b
Subproblem 2
Set the factor '(8a + 5b)' equal to zero and attempt to solve:

Simplifying
8a + 5b = 0

Solving
8a + 5b = 0

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

Add '-5b' to each side of the equation.
8a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
8a + 0 = 0 + -5b
8a = 0 + -5b
Remove the zero:
8a = -5b

Divide each side by '8'.
a = -0.625b

Simplifying
a = -0.625b
Solution
a = {b, -0.625b}