z^2-14z=15

Solution for z^2-14z=15 equation:

Simplifying
z2 + -14z = 15

Reorder the terms:
-14z + z2 = 15

Solving
-14z + z2 = 15

Solving for variable 'z'.

Reorder the terms:
-15 + -14z + z2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -14z + z2 = 0

Factor a trinomial.
(-1 + -1z)(15 + -1z) = 0

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 '(15 + -1z)' equal to zero and attempt to solve:

Simplifying
15 + -1z = 0

Solving
15 + -1z = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1z = 0 + -15
-1z = 0 + -15

Combine like terms: 0 + -15 = -15
-1z = -15

Divide each side by '-1'.
z = 15

Simplifying
z = 15
Solution
z = {-1, 15}