3z^2+3=6z

Solution for 3z^2+3=6z equation:

Simplifying
3z2 + 3 = 6z

Reorder the terms:
3 + 3z2 = 6z

Solving
3 + 3z2 = 6z

Solving for variable 'z'.

Reorder the terms:
3 + -6z + 3z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
3 + -6z + 3z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2z + z2) = 0

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

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

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

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

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

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

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

Simplifying
z = 1
Solution
z = {1, 1}