2a^2x^2+5ax-3=0

Solution for 2a^2x^2+5ax-3=0 equation:

Simplifying
2a2x2 + 5ax + -3 = 0

Reorder the terms:
-3 + 5ax + 2a2x2 = 0

Solving
-3 + 5ax + 2a2x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1ax)(1 + -2ax) = 0

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

Simplifying
-3 + -1ax = 0

Solving
-3 + -1ax = 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 + -1ax = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1ax = 0 + 3
-1ax = 0 + 3

Combine like terms: 0 + 3 = 3
-1ax = 3

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

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

Simplifying
1 + -2ax = 0

Solving
1 + -2ax = 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 + -2ax = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2ax = 0 + -1
-2ax = 0 + -1

Combine like terms: 0 + -1 = -1
-2ax = -1

Divide each side by '-2x'.
a = 0.5x-1

Simplifying
a = 0.5x-1
Solution
a = {-3x-1, 0.5x-1}