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

Solution for (1-2a)(a+3)=0 equation:

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

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

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

Combine like terms: 1a + -6a = -5a
(3 + -5a + -2a2) = 0

Solving
3 + -5a + -2a2 = 0

Solving for variable 'a'.

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

Simplifying
3 + a = 0

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

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

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

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