2z(3z+11)=8

Solution for 2z(3z+11)=8 equation:

Simplifying
2z(3z + 11) = 8

Reorder the terms:
2z(11 + 3z) = 8
(11 * 2z + 3z * 2z) = 8
(22z + 6z2) = 8

Solving
22z + 6z2 = 8

Solving for variable 'z'.

Reorder the terms:
-8 + 22z + 6z2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 22z + 6z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 11z + 3z2) = 0

Factor a trinomial.
2((-4 + -1z)(1 + -3z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4
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 = {-4, 0.3333333333}