a^2+10ab+21b^2=0

Solution for a^2+10ab+21b^2=0 equation:

Simplifying
a2 + 10ab + 21b2 = 0

Reorder the terms:
10ab + a2 + 21b2 = 0

Solving
10ab + a2 + 21b2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
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 = {-3b, -7b}