z^2-11z=42

Solution for z^2-11z=42 equation:

Simplifying
z2 + -11z = 42

Reorder the terms:
-11z + z2 = 42

Solving
-11z + z2 = 42

Solving for variable 'z'.

Reorder the terms:
-42 + -11z + z2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -11z + z2 = 0

Factor a trinomial.
(-3 + -1z)(14 + -1z) = 0

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 '(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
Solution
z = {-3, 14}