a^2+14ab+49b^2=0

Solution for a^2+14ab+49b^2=0 equation:

Simplifying
a2 + 14ab + 49b2 = 0

Reorder the terms:
14ab + a2 + 49b2 = 0

Solving
14ab + a2 + 49b2 = 0

Solving for variable 'a'.

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

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