3a^2x^2-4ax=7

Solution for 3a^2x^2-4ax=7 equation:

Simplifying
3a2x2 + -4ax = 7

Reorder the terms:
-4ax + 3a2x2 = 7

Solving
-4ax + 3a2x2 = 7

Solving for variable 'a'.

Reorder the terms:
-7 + -4ax + 3a2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -4ax + 3a2x2 = 0

Factor a trinomial.
(-1 + -1ax)(7 + -3ax) = 0

Subproblem 1
Set the factor '(-1 + -1ax)' equal to zero and attempt to solve:

Simplifying
-1 + -1ax = 0

Solving
-1 + -1ax = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1ax = 0 + 1
-1ax = 0 + 1

Combine like terms: 0 + 1 = 1
-1ax = 1

Divide each side by '-1x'.
a = -1x-1

Simplifying
a = -1x-1
Subproblem 2
Set the factor '(7 + -3ax)' equal to zero and attempt to solve:

Simplifying
7 + -3ax = 0

Solving
7 + -3ax = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3ax = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3ax = 0 + -7
-3ax = 0 + -7

Combine like terms: 0 + -7 = -7
-3ax = -7

Divide each side by '-3x'.
a = 2.333333333x-1

Simplifying
a = 2.333333333x-1
Solution
a = {-1x-1, 2.333333333x-1}