z^2-19z+90.25=156.25

Solution for z^2-19z+90.25=156.25 equation:

Simplifying
z2 + -19z + 90.25 = 156.25

Reorder the terms:
90.25 + -19z + z2 = 156.25

Solving
90.25 + -19z + z2 = 156.25

Solving for variable 'z'.

Reorder the terms:
90.25 + -156.25 + -19z + z2 = 156.25 + -156.25

Combine like terms: 90.25 + -156.25 = -66
-66 + -19z + z2 = 156.25 + -156.25

Combine like terms: 156.25 + -156.25 = 0.00
-66 + -19z + z2 = 0.00

Factor a trinomial.
(-3 + -1z)(22 + -1z) = 0.00

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

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(22 + -1z)' equal to zero and attempt to solve:

Simplifying
22 + -1z = 0

Solving
22 + -1z = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1z = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1z = 0 + -22
-1z = 0 + -22

Combine like terms: 0 + -22 = -22
-1z = -22

Divide each side by '-1'.
z = 22

Simplifying
z = 22
Solution
z = {-3, 22}