3z^2-48z-51=0

Solution for 3z^2-48z-51=0 equation:

Simplifying
3z2 + -48z + -51 = 0

Reorder the terms:
-51 + -48z + 3z2 = 0

Solving
-51 + -48z + 3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-17 + -16z + z2) = 0

Factor a trinomial.
3((-1 + -1z)(17 + -1z)) = 0

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

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 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 + -1z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1z = 0 + 1
-1z = 0 + 1

Combine like terms: 0 + 1 = 1
-1z = 1

Divide each side by '-1'.
z = -1

Simplifying
z = -1
Subproblem 2
Set the factor '(17 + -1z)' equal to zero and attempt to solve:

Simplifying
17 + -1z = 0

Solving
17 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-17' to each side of the equation.
17 + -17 + -1z = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1z = 0 + -17
-1z = 0 + -17

Combine like terms: 0 + -17 = -17
-1z = -17

Divide each side by '-1'.
z = 17

Simplifying
z = 17
Solution
z = {-1, 17}