100a^2-140ab+49b^2=0

Solution for 100a^2-140ab+49b^2=0 equation:

Simplifying
100a2 + -140ab + 49b2 = 0

Reorder the terms:
-140ab + 100a2 + 49b2 = 0

Solving
-140ab + 100a2 + 49b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(10a + -7b)(10a + -7b) = 0

Subproblem 1
Set the factor '(10a + -7b)' equal to zero and attempt to solve:

Simplifying
10a + -7b = 0

Solving
10a + -7b = 0

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

Add '7b' to each side of the equation.
10a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
10a + 0 = 0 + 7b
10a = 0 + 7b
Remove the zero:
10a = 7b

Divide each side by '10'.
a = 0.7b

Simplifying
a = 0.7b
Subproblem 2
Set the factor '(10a + -7b)' equal to zero and attempt to solve:

Simplifying
10a + -7b = 0

Solving
10a + -7b = 0

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

Add '7b' to each side of the equation.
10a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
10a + 0 = 0 + 7b
10a = 0 + 7b
Remove the zero:
10a = 7b

Divide each side by '10'.
a = 0.7b

Simplifying
a = 0.7b
Solution
a = {0.7b, 0.7b}