6a(2a-1)-(3a^2-3a)=

Solution for 6a(2a-1)-(3a^2-3a)= equation:

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

Reorder the terms:
6a(-1 + 2a) + -1(3a2 + -3a) = 0
(-1 * 6a + 2a * 6a) + -1(3a2 + -3a) = 0
(-6a + 12a2) + -1(3a2 + -3a) = 0

Reorder the terms:
-6a + 12a2 + -1(-3a + 3a2) = 0
-6a + 12a2 + (-3a * -1 + 3a2 * -1) = 0
-6a + 12a2 + (3a + -3a2) = 0

Reorder the terms:
-6a + 3a + 12a2 + -3a2 = 0

Combine like terms: -6a + 3a = -3a
-3a + 12a2 + -3a2 = 0

Combine like terms: 12a2 + -3a2 = 9a2
-3a + 9a2 = 0

Solving
-3a + 9a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-1 + 3a) = 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 + 3a)' equal to zero and attempt to solve:

Simplifying
-1 + 3a = 0

Solving
-1 + 3a = 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 + 3a = 0 + 1

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

Combine like terms: 0 + 1 = 1
3a = 1

Divide each side by '3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {0, 0.3333333333}