2z(3z+1)=-9z-3

Solution for 2z(3z+1)=-9z-3 equation:

Simplifying
2z(3z + 1) = -9z + -3

Reorder the terms:
2z(1 + 3z) = -9z + -3
(1 * 2z + 3z * 2z) = -9z + -3
(2z + 6z2) = -9z + -3

Reorder the terms:
2z + 6z2 = -3 + -9z

Solving
2z + 6z2 = -3 + -9z

Solving for variable 'z'.

Reorder the terms:
3 + 2z + 9z + 6z2 = -3 + -9z + 3 + 9z

Combine like terms: 2z + 9z = 11z
3 + 11z + 6z2 = -3 + -9z + 3 + 9z

Reorder the terms:
3 + 11z + 6z2 = -3 + 3 + -9z + 9z

Combine like terms: -3 + 3 = 0
3 + 11z + 6z2 = 0 + -9z + 9z
3 + 11z + 6z2 = -9z + 9z

Combine like terms: -9z + 9z = 0
3 + 11z + 6z2 = 0

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

Subproblem 1
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
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 = {-1.5, -0.3333333333}