z^2+2z+3z^2=

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

Simplifying
z2 + 2z + 3z2 = 0

Reorder the terms:
2z + z2 + 3z2 = 0

Combine like terms: z2 + 3z2 = 4z2
2z + 4z2 = 0

Solving
2z + 4z2 = 0

Solving for variable 'z'.

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

Ignore the factor 2.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

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

Simplifying
1 + 2z = 0

Solving
1 + 2z = 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 + 2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2z = 0 + -1
2z = 0 + -1

Combine like terms: 0 + -1 = -1
2z = -1

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {0, -0.5}