3z(3z+14)=72

Solution for 3z(3z+14)=72 equation:

Simplifying
3z(3z + 14) = 72

Reorder the terms:
3z(14 + 3z) = 72
(14 * 3z + 3z * 3z) = 72
(42z + 9z2) = 72

Solving
42z + 9z2 = 72

Solving for variable 'z'.

Reorder the terms:
-72 + 42z + 9z2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 42z + 9z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 14z + 3z2) = 0

Factor a trinomial.
3((-6 + -1z)(4 + -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 '(4 + -3z)' equal to zero and attempt to solve:

Simplifying
4 + -3z = 0

Solving
4 + -3z = 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 + -3z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3z = 0 + -4
-3z = 0 + -4

Combine like terms: 0 + -4 = -4
-3z = -4

Divide each side by '-3'.
z = 1.333333333

Simplifying
z = 1.333333333
Solution
z = {-6, 1.333333333}