2(2a^2-4a)+3=0

Solution for 2(2a^2-4a)+3=0 equation:

Simplifying
2(2a2 + -4a) + 3 = 0

Reorder the terms:
2(-4a + 2a2) + 3 = 0
(-4a * 2 + 2a2 * 2) + 3 = 0
(-8a + 4a2) + 3 = 0

Reorder the terms:
3 + -8a + 4a2 = 0

Solving
3 + -8a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -2a)(3 + -2a) = 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 '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

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

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

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

Simplifying
a = 1.5
Solution
a = {0.5, 1.5}