3a+4a(a-1)=

Solution for 3a+4a(a-1)= equation:

Simplifying
3a + 4a(a + -1) = 0

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

Combine like terms: 3a + -4a = -1a
-1a + 4a2 = 0

Solving
-1a + 4a2 = 0

Solving for variable 'a'.

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

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}