2z^2+11z+1=7

Solution for 2z^2+11z+1=7 equation:

Simplifying
2z2 + 11z + 1 = 7

Reorder the terms:
1 + 11z + 2z2 = 7

Solving
1 + 11z + 2z2 = 7

Solving for variable 'z'.

Reorder the terms:
1 + -7 + 11z + 2z2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + 11z + 2z2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + 11z + 2z2 = 0

Factor a trinomial.
(-6 + -1z)(1 + -2z) = 0

Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
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 = {-6, 0.5}