a^2+9ab+14b^2=

Solution for a^2+9ab+14b^2= equation:

Simplifying
a2 + 9ab + 14b2 = 0

Reorder the terms:
9ab + a2 + 14b2 = 0

Solving
9ab + a2 + 14b2 = 0

Solving for variable 'a'.

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

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

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

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

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

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

Simplifying
a + 7b = 0

Solving
a + 7b = 0

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

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

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

Simplifying
a = -7b
Solution
a = {-2b, -7b}