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.
(-14 + -1z)(3 + -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 '(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
Solution
z = {-14, 3}