(6a^2)*x^2-11ax=10

Solution for (6a^2)*x^2-11ax=10 equation:

Simplifying
(6a2) * x2 + -11ax = 10

Remove parenthesis around (6a2)
6a2 * x2 + -11ax = 10

Multiply a2 * x2
6a2x2 + -11ax = 10

Reorder the terms:
-11ax + 6a2x2 = 10

Solving
-11ax + 6a2x2 = 10

Solving for variable 'a'.

Reorder the terms:
-10 + -11ax + 6a2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -11ax + 6a2x2 = 0

Factor a trinomial.
(-2 + -3ax)(5 + -2ax) = 0

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

Simplifying
-2 + -3ax = 0

Solving
-2 + -3ax = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3ax = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3ax = 0 + 2
-3ax = 0 + 2

Combine like terms: 0 + 2 = 2
-3ax = 2

Divide each side by '-3x'.
a = -0.6666666667x-1

Simplifying
a = -0.6666666667x-1
Subproblem 2
Set the factor '(5 + -2ax)' equal to zero and attempt to solve:

Simplifying
5 + -2ax = 0

Solving
5 + -2ax = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2ax = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2ax = 0 + -5
-2ax = 0 + -5

Combine like terms: 0 + -5 = -5
-2ax = -5

Divide each side by '-2x'.
a = 2.5x-1

Simplifying
a = 2.5x-1
Solution
a = {-0.6666666667x-1, 2.5x-1}