5z^2+10z-120=0

Solution for 5z^2+10z-120=0 equation:

Simplifying
5z2 + 10z + -120 = 0

Reorder the terms:
-120 + 10z + 5z2 = 0

Solving
-120 + 10z + 5z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + 2z + z2) = 0

Factor a trinomial.
5((-6 + -1z)(4 + -1z)) = 0

Ignore the factor 5.
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 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 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 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-6, 4}