3z(3z+16)=36

Solution for 3z(3z+16)=36 equation:

Simplifying
3z(3z + 16) = 36

Reorder the terms:
3z(16 + 3z) = 36
(16 * 3z + 3z * 3z) = 36
(48z + 9z2) = 36

Solving
48z + 9z2 = 36

Solving for variable 'z'.

Reorder the terms:
-36 + 48z + 9z2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 48z + 9z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 16z + 3z2) = 0

Factor a trinomial.
3((-6 + -1z)(2 + -3z)) = 0

Ignore the factor 3.
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 '(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 = {-6, 0.6666666667}