=3a(2a*2+1)

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

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

Reorder the terms for easier multiplication:
0 = 3a(2 * 2a + 1)

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

Reorder the terms:
0 = 3a(1 + 4a)
0 = (1 * 3a + 4a * 3a)
0 = (3a + 12a2)

Solving
0 = 3a + 12a2

Solving for variable 'a'.
Remove the zero:
-3a + -12a2 = 3a + 12a2 + -3a + -12a2

Reorder the terms:
-3a + -12a2 = 3a + -3a + 12a2 + -12a2

Combine like terms: 3a + -3a = 0
-3a + -12a2 = 0 + 12a2 + -12a2
-3a + -12a2 = 12a2 + -12a2

Combine like terms: 12a2 + -12a2 = 0
-3a + -12a2 = 0

Factor out the Greatest Common Factor (GCF), '-3a'.
-3a(1 + 4a) = 0

Ignore the factor -3.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0
Subproblem 2
Set the factor '(1 + 4a)' equal to zero and attempt to solve:

Simplifying
1 + 4a = 0

Solving
1 + 4a = 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 + 4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4a = 0 + -1
4a = 0 + -1

Combine like terms: 0 + -1 = -1
4a = -1

Divide each side by '4'.
a = -0.25

Simplifying
a = -0.25
Solution
a = {0, -0.25}