3a^2=6a-3

Solution for 3a^2=6a-3 equation:

Simplifying
3a2 = 6a + -3

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

Solving
3a2 = -3 + 6a

Solving for variable 'a'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2a + a2) = 0

Factor a trinomial.
3((1 + -1a)(1 + -1a)) = 0

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

Simplifying
1 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 1

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

Simplifying
1 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {1, 1}