9Z^2+48Z=36

Solution for 9Z^2+48Z=36 equation:

Simplifying
9Z2 + 48Z = 36

Reorder the terms:
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}