25z^2+55z-102=0

Solution for 25z^2+55z-102=0 equation:

Simplifying
25z2 + 55z + -102 = 0

Reorder the terms:
-102 + 55z + 25z2 = 0

Solving
-102 + 55z + 25z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-17 + -5z)(6 + -5z) = 0

Subproblem 1
Set the factor '(-17 + -5z)' equal to zero and attempt to solve:

Simplifying
-17 + -5z = 0

Solving
-17 + -5z = 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 + -5z = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -5z = 0 + 17
-5z = 0 + 17

Combine like terms: 0 + 17 = 17
-5z = 17

Divide each side by '-5'.
z = -3.4

Simplifying
z = -3.4
Subproblem 2
Set the factor '(6 + -5z)' equal to zero and attempt to solve:

Simplifying
6 + -5z = 0

Solving
6 + -5z = 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 + -5z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5z = 0 + -6
-5z = 0 + -6

Combine like terms: 0 + -6 = -6
-5z = -6

Divide each side by '-5'.
z = 1.2

Simplifying
z = 1.2
Solution
z = {-3.4, 1.2}