a(2a-3)=2

Solution for a(2a-3)=2 equation:

Simplifying
a(2a + -3) = 2

Reorder the terms:
a(-3 + 2a) = 2
(-3 * a + 2a * a) = 2
(-3a + 2a2) = 2

Solving
-3a + 2a2 = 2

Solving for variable 'a'.

Reorder the terms:
-2 + -3a + 2a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -3a + 2a2 = 0

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

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

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

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

Simplifying
a = -0.5
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

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

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

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

Simplifying
a = 2
Solution
a = {-0.5, 2}