6a^2+19ab-7b^2=

Solution for 6a^2+19ab-7b^2= equation:

Simplifying
6a2 + 19ab + -7b2 = 0

Reorder the terms:
19ab + 6a2 + -7b2 = 0

Solving
19ab + 6a2 + -7b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -1b)(2a + 7b) = 0

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

Simplifying
3a + -1b = 0

Solving
3a + -1b = 0

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

Add 'b' to each side of the equation.
3a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
3a + 0 = 0 + b
3a = 0 + b
Remove the zero:
3a = b

Divide each side by '3'.
a = 0.3333333333b

Simplifying
a = 0.3333333333b
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 = {0.3333333333b, -3.5b}