z^2+9z-90=(z-6)

Solution for z^2+9z-90=(z-6) equation:

Simplifying
z2 + 9z + -90 = (z + -6)

Reorder the terms:
-90 + 9z + z2 = (z + -6)

Reorder the terms:
-90 + 9z + z2 = (-6 + z)

Remove parenthesis around (-6 + z)
-90 + 9z + z2 = -6 + z

Solving
-90 + 9z + z2 = -6 + z

Solving for variable 'z'.

Reorder the terms:
-90 + 6 + 9z + -1z + z2 = -6 + z + 6 + -1z

Combine like terms: -90 + 6 = -84
-84 + 9z + -1z + z2 = -6 + z + 6 + -1z

Combine like terms: 9z + -1z = 8z
-84 + 8z + z2 = -6 + z + 6 + -1z

Reorder the terms:
-84 + 8z + z2 = -6 + 6 + z + -1z

Combine like terms: -6 + 6 = 0
-84 + 8z + z2 = 0 + z + -1z
-84 + 8z + z2 = z + -1z

Combine like terms: z + -1z = 0
-84 + 8z + z2 = 0

Factor a trinomial.
(-14 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-14 + -1z)' equal to zero and attempt to solve:

Simplifying
-14 + -1z = 0

Solving
-14 + -1z = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1z = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1z = 0 + 14
-1z = 0 + 14

Combine like terms: 0 + 14 = 14
-1z = 14

Divide each side by '-1'.
z = -14

Simplifying
z = -14
Subproblem 2
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
Solution
z = {-14, 6}