10a^2x^2+11ax-6=0

Solution for 10a^2x^2+11ax-6=0 equation:

Simplifying
10a2x2 + 11ax + -6 = 0

Reorder the terms:
-6 + 11ax + 10a2x2 = 0

Solving
-6 + 11ax + 10a2x2 = 0

Solving for variable 'a'.

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

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

Simplifying
-3 + -2ax = 0

Solving
-3 + -2ax = 0

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

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

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

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

Divide each side by '-2x'.
a = -1.5x-1

Simplifying
a = -1.5x-1
Subproblem 2
Set the factor '(2 + -5ax)' equal to zero and attempt to solve:

Simplifying
2 + -5ax = 0

Solving
2 + -5ax = 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 + -5ax = 0 + -2

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

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

Divide each side by '-5x'.
a = 0.4x-1

Simplifying
a = 0.4x-1
Solution
a = {-1.5x-1, 0.4x-1}