a^2-11ab+28b^2=0

Solution for a^2-11ab+28b^2=0 equation:

Simplifying
a2 + -11ab + 28b2 = 0

Reorder the terms:
-11ab + a2 + 28b2 = 0

Solving
-11ab + a2 + 28b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -7b)(a + -4b) = 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 + -4b)' equal to zero and attempt to solve:

Simplifying
a + -4b = 0

Solving
a + -4b = 0

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

Add '4b' to each side of the equation.
a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
a + 0 = 0 + 4b
a = 0 + 4b
Remove the zero:
a = 4b

Simplifying
a = 4b
Solution
a = {7b, 4b}