7a^2b^2-70ab+168=

Solution for 7a^2b^2-70ab+168= equation:

Simplifying
7a2b2 + -70ab + 168 = 0

Reorder the terms:
168 + -70ab + 7a2b2 = 0

Solving
168 + -70ab + 7a2b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(24 + -10ab + a2b2) = 0

Factor a trinomial.
7((4 + -1ab)(6 + -1ab)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(4 + -1ab)' equal to zero and attempt to solve:

Simplifying
4 + -1ab = 0

Solving
4 + -1ab = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1ab = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1ab = 0 + -4
-1ab = 0 + -4

Combine like terms: 0 + -4 = -4
-1ab = -4

Divide each side by '-1b'.
a = 4b-1

Simplifying
a = 4b-1
Subproblem 2
Set the factor '(6 + -1ab)' equal to zero and attempt to solve:

Simplifying
6 + -1ab = 0

Solving
6 + -1ab = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1ab = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1ab = 0 + -6
-1ab = 0 + -6

Combine like terms: 0 + -6 = -6
-1ab = -6

Divide each side by '-1b'.
a = 6b-1

Simplifying
a = 6b-1
Solution
a = {4b-1, 6b-1}