12a^2+40ab-7b^2=

Solution for 12a^2+40ab-7b^2= equation:

Simplifying
12a2 + 40ab + -7b2 = 0

Reorder the terms:
40ab + 12a2 + -7b2 = 0

Solving
40ab + 12a2 + -7b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6a + -1b)(2a + 7b) = 0

Subproblem 1
Set the factor '(6a + -1b)' equal to zero and attempt to solve:

Simplifying
6a + -1b = 0

Solving
6a + -1b = 0

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

Add 'b' to each side of the equation.
6a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
6a + 0 = 0 + b
6a = 0 + b
Remove the zero:
6a = b

Divide each side by '6'.
a = 0.1666666667b

Simplifying
a = 0.1666666667b
Subproblem 2
Set the factor '(2a + 7b)' equal to zero and attempt to solve:

Simplifying
2a + 7b = 0

Solving
2a + 7b = 0

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

Add '-7b' to each side of the equation.
2a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
2a + 0 = 0 + -7b
2a = 0 + -7b
Remove the zero:
2a = -7b

Divide each side by '2'.
a = -3.5b

Simplifying
a = -3.5b
Solution
a = {0.1666666667b, -3.5b}