3a^2+2ab-21b^2=

Solution for 3a^2+2ab-21b^2= equation:

Simplifying
3a2 + 2ab + -21b2 = 0

Reorder the terms:
2ab + 3a2 + -21b2 = 0

Solving
2ab + 3a2 + -21b2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(a + 3b)' equal to zero and attempt to solve:

Simplifying
a + 3b = 0

Solving
a + 3b = 0

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

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

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

Simplifying
a = -3b
Solution
a = {2.333333333b, -3b}