z(2z+1)=6

Solution for z(2z+1)=6 equation:

Simplifying
z(2z + 1) = 6

Reorder the terms:
z(1 + 2z) = 6
(1 * z + 2z * z) = 6
(1z + 2z2) = 6

Solving
1z + 2z2 = 6

Solving for variable 'z'.

Reorder the terms:
-6 + 1z + 2z2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 1z + 2z2 = 0

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

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

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

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

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

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {-2, 1.5}