3z^2+2z+6=7

Solution for 3z^2+2z+6=7 equation:

Simplifying
3z2 + 2z + 6 = 7

Reorder the terms:
6 + 2z + 3z2 = 7

Solving
6 + 2z + 3z2 = 7

Solving for variable 'z'.

Reorder the terms:
6 + -7 + 2z + 3z2 = 7 + -7

Combine like terms: 6 + -7 = -1
-1 + 2z + 3z2 = 7 + -7

Combine like terms: 7 + -7 = 0
-1 + 2z + 3z2 = 0

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

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 + -3z)' equal to zero and attempt to solve:

Simplifying
1 + -3z = 0

Solving
1 + -3z = 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 + -3z = 0 + -1

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

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

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Solution
z = {-1, 0.3333333333}