z^2-121=(z+11)

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Solution for z^2-121=(z+11) equation:


Simplifying
z2 + -121 = (z + 11)

Reorder the terms:
-121 + z2 = (z + 11)

Reorder the terms:
-121 + z2 = (11 + z)

Remove parenthesis around (11 + z)
-121 + z2 = 11 + z

Solving
-121 + z2 = 11 + z

Solving for variable 'z'.

Reorder the terms:
-121 + -11 + -1z + z2 = 11 + z + -11 + -1z

Combine like terms: -121 + -11 = -132
-132 + -1z + z2 = 11 + z + -11 + -1z

Reorder the terms:
-132 + -1z + z2 = 11 + -11 + z + -1z

Combine like terms: 11 + -11 = 0
-132 + -1z + z2 = 0 + z + -1z
-132 + -1z + z2 = z + -1z

Combine like terms: z + -1z = 0
-132 + -1z + z2 = 0

Factor a trinomial.
(-11 + -1z)(12 + -1z) = 0


Subproblem 1
Set the factor '(-11 + -1z)' equal to zero and attempt to solve:

Simplifying
-11 + -1z = 0

Solving
-11 + -1z = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1z = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1z = 0 + 11
-1z = 0 + 11

Combine like terms: 0 + 11 = 11
-1z = 11

Divide each side by '-1'.
z = -11

Simplifying
z = -11

Subproblem 2
Set the factor '(12 + -1z)' equal to zero and attempt to solve:

Simplifying
12 + -1z = 0

Solving
12 + -1z = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1z = 0 + -12
-1z = 0 + -12

Combine like terms: 0 + -12 = -12
-1z = -12

Divide each side by '-1'.
z = 12

Simplifying
z = 12
Solution
z = {-11, 12}

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