15a^2-17ab-4b^2=

Solution for 15a^2-17ab-4b^2= equation:

Simplifying
15a2 + -17ab + -4b2 = 0

Reorder the terms:
-17ab + 15a2 + -4b2 = 0

Solving
-17ab + 15a2 + -4b2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve:

Simplifying
3a + -4b = 0

Solving
3a + -4b = 0

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

Add '4b' to each side of the equation.
3a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
3a + 0 = 0 + 4b
3a = 0 + 4b
Remove the zero:
3a = 4b

Divide each side by '3'.
a = 1.333333333b

Simplifying
a = 1.333333333b
Subproblem 2
Set the factor '(5a + b)' equal to zero and attempt to solve:

Simplifying
5a + b = 0

Solving
5a + b = 0

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

Add '-1b' to each side of the equation.
5a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
5a + 0 = 0 + -1b
5a = 0 + -1b
Remove the zero:
5a = -1b

Divide each side by '5'.
a = -0.2b

Simplifying
a = -0.2b
Solution
a = {1.333333333b, -0.2b}