12a^2+13ab-35b^2=

Solution for 12a^2+13ab-35b^2= equation:

Simplifying
12a2 + 13ab + -35b2 = 0

Reorder the terms:
13ab + 12a2 + -35b2 = 0

Solving
13ab + 12a2 + -35b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -5b)(3a + 7b) = 0

Subproblem 1
Set the factor '(4a + -5b)' equal to zero and attempt to solve:

Simplifying
4a + -5b = 0

Solving
4a + -5b = 0

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

Add '5b' to each side of the equation.
4a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
4a + 0 = 0 + 5b
4a = 0 + 5b
Remove the zero:
4a = 5b

Divide each side by '4'.
a = 1.25b

Simplifying
a = 1.25b
Subproblem 2
Set the factor '(3a + 7b)' equal to zero and attempt to solve:

Simplifying
3a + 7b = 0

Solving
3a + 7b = 0

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

Add '-7b' to each side of the equation.
3a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
3a + 0 = 0 + -7b
3a = 0 + -7b
Remove the zero:
3a = -7b

Divide each side by '3'.
a = -2.333333333b

Simplifying
a = -2.333333333b
Solution
a = {1.25b, -2.333333333b}