12a^2-17ab-5b^2=

Solution for 12a^2-17ab-5b^2= equation:

Simplifying
12a2 + -17ab + -5b2 = 0

Reorder the terms:
-17ab + 12a2 + -5b2 = 0

Solving
-17ab + 12a2 + -5b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -5b)(4a + b) = 0

Subproblem 1
Set the factor '(3a + -5b)' equal to zero and attempt to solve:

Simplifying
3a + -5b = 0

Solving
3a + -5b = 0

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

Add '5b' to each side of the equation.
3a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
3a + 0 = 0 + 5b
3a = 0 + 5b
Remove the zero:
3a = 5b

Divide each side by '3'.
a = 1.666666667b

Simplifying
a = 1.666666667b
Subproblem 2
Set the factor '(4a + b)' equal to zero and attempt to solve:

Simplifying
4a + b = 0

Solving
4a + b = 0

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

Add '-1b' to each side of the equation.
4a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
4a + 0 = 0 + -1b
4a = 0 + -1b
Remove the zero:
4a = -1b

Divide each side by '4'.
a = -0.25b

Simplifying
a = -0.25b
Solution
a = {1.666666667b, -0.25b}