(m-11)(m+3)=m-11

Solution for (m-11)(m+3)=m-11 equation:

Simplifying
(m + -11)(m + 3) = m + -11

Reorder the terms:
(-11 + m)(m + 3) = m + -11

Reorder the terms:
(-11 + m)(3 + m) = m + -11

Multiply (-11 + m) * (3 + m)
(-11(3 + m) + m(3 + m)) = m + -11
((3 * -11 + m * -11) + m(3 + m)) = m + -11
((-33 + -11m) + m(3 + m)) = m + -11
(-33 + -11m + (3 * m + m * m)) = m + -11
(-33 + -11m + (3m + m2)) = m + -11

Combine like terms: -11m + 3m = -8m
(-33 + -8m + m2) = m + -11

Reorder the terms:
-33 + -8m + m2 = -11 + m

Solving
-33 + -8m + m2 = -11 + m

Solving for variable 'm'.

Reorder the terms:
-33 + 11 + -8m + -1m + m2 = -11 + m + 11 + -1m

Combine like terms: -33 + 11 = -22
-22 + -8m + -1m + m2 = -11 + m + 11 + -1m

Combine like terms: -8m + -1m = -9m
-22 + -9m + m2 = -11 + m + 11 + -1m

Reorder the terms:
-22 + -9m + m2 = -11 + 11 + m + -1m

Combine like terms: -11 + 11 = 0
-22 + -9m + m2 = 0 + m + -1m
-22 + -9m + m2 = m + -1m

Combine like terms: m + -1m = 0
-22 + -9m + m2 = 0

Factor a trinomial.
(-2 + -1m)(11 + -1m) = 0

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

Simplifying
-2 + -1m = 0

Solving
-2 + -1m = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1m = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1m = 0 + 2
-1m = 0 + 2

Combine like terms: 0 + 2 = 2
-1m = 2

Divide each side by '-1'.
m = -2

Simplifying
m = -2
Subproblem 2
Set the factor '(11 + -1m)' equal to zero and attempt to solve:

Simplifying
11 + -1m = 0

Solving
11 + -1m = 0

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

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

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

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

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

Simplifying
m = 11
Solution
m = {-2, 11}