3z(2z+1)=4z+2

Solution for 3z(2z+1)=4z+2 equation:

Simplifying
3z(2z + 1) = 4z + 2

Reorder the terms:
3z(1 + 2z) = 4z + 2
(1 * 3z + 2z * 3z) = 4z + 2
(3z + 6z2) = 4z + 2

Reorder the terms:
3z + 6z2 = 2 + 4z

Solving
3z + 6z2 = 2 + 4z

Solving for variable 'z'.

Reorder the terms:
-2 + 3z + -4z + 6z2 = 2 + 4z + -2 + -4z

Combine like terms: 3z + -4z = -1z
-2 + -1z + 6z2 = 2 + 4z + -2 + -4z

Reorder the terms:
-2 + -1z + 6z2 = 2 + -2 + 4z + -4z

Combine like terms: 2 + -2 = 0
-2 + -1z + 6z2 = 0 + 4z + -4z
-2 + -1z + 6z2 = 4z + -4z

Combine like terms: 4z + -4z = 0
-2 + -1z + 6z2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve:

Simplifying
2 + -3z = 0

Solving
2 + -3z = 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 + -3z = 0 + -2

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

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

Divide each side by '-3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Solution
z = {-0.5, 0.6666666667}