(m-13)(m+6)=m-13

Solution for (m-13)(m+6)=m-13 equation:

Simplifying
(m + -13)(m + 6) = m + -13

Reorder the terms:
(-13 + m)(m + 6) = m + -13

Reorder the terms:
(-13 + m)(6 + m) = m + -13

Multiply (-13 + m) * (6 + m)
(-13(6 + m) + m(6 + m)) = m + -13
((6 * -13 + m * -13) + m(6 + m)) = m + -13
((-78 + -13m) + m(6 + m)) = m + -13
(-78 + -13m + (6 * m + m * m)) = m + -13
(-78 + -13m + (6m + m2)) = m + -13

Combine like terms: -13m + 6m = -7m
(-78 + -7m + m2) = m + -13

Reorder the terms:
-78 + -7m + m2 = -13 + m

Solving
-78 + -7m + m2 = -13 + m

Solving for variable 'm'.

Reorder the terms:
-78 + 13 + -7m + -1m + m2 = -13 + m + 13 + -1m

Combine like terms: -78 + 13 = -65
-65 + -7m + -1m + m2 = -13 + m + 13 + -1m

Combine like terms: -7m + -1m = -8m
-65 + -8m + m2 = -13 + m + 13 + -1m

Reorder the terms:
-65 + -8m + m2 = -13 + 13 + m + -1m

Combine like terms: -13 + 13 = 0
-65 + -8m + m2 = 0 + m + -1m
-65 + -8m + m2 = m + -1m

Combine like terms: m + -1m = 0
-65 + -8m + m2 = 0

Factor a trinomial.
(-5 + -1m)(13 + -1m) = 0

Subproblem 1
Set the factor '(-5 + -1m)' equal to zero and attempt to solve:

Simplifying
-5 + -1m = 0

Solving
-5 + -1m = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1m = 0 + 5
-1m = 0 + 5

Combine like terms: 0 + 5 = 5
-1m = 5

Divide each side by '-1'.
m = -5

Simplifying
m = -5
Subproblem 2
Set the factor '(13 + -1m)' equal to zero and attempt to solve:

Simplifying
13 + -1m = 0

Solving
13 + -1m = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1m = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1m = 0 + -13
-1m = 0 + -13

Combine like terms: 0 + -13 = -13
-1m = -13

Divide each side by '-1'.
m = 13

Simplifying
m = 13
Solution
m = {-5, 13}