(2a-3)(2a+1)=

Solution for (2a-3)(2a+1)= equation:

Simplifying
(2a + -3)(2a + 1) = 0

Reorder the terms:
(-3 + 2a)(2a + 1) = 0

Reorder the terms:
(-3 + 2a)(1 + 2a) = 0

Multiply (-3 + 2a) * (1 + 2a)
(-3(1 + 2a) + 2a * (1 + 2a)) = 0
((1 * -3 + 2a * -3) + 2a * (1 + 2a)) = 0
((-3 + -6a) + 2a * (1 + 2a)) = 0
(-3 + -6a + (1 * 2a + 2a * 2a)) = 0
(-3 + -6a + (2a + 4a2)) = 0

Combine like terms: -6a + 2a = -4a
(-3 + -4a + 4a2) = 0

Solving
-3 + -4a + 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}