m[m-7]=m-7

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Solution for m[m-7]=m-7 equation: 


Simplifying
m[m + -7] = m + -7

Reorder the terms:
m[-7 + m] = m + -7
[-7 * m + m * m] = m + -7
[-7m + m2] = m + -7

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

Solving
-7m + m2 = -7 + m

Solving for variable 'm'.

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

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

Reorder the terms:
7 + -8m + m2 = -7 + 7 + m + -1m

Combine like terms: -7 + 7 = 0
7 + -8m + m2 = 0 + m + -1m
7 + -8m + m2 = m + -1m

Combine like terms: m + -1m = 0
7 + -8m + m2 = 0

Factor a trinomial.
(1 + -1m)(7 + -1m) = 0


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

Simplifying
1 + -1m = 0

Solving
1 + -1m = 0

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

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

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

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

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

Simplifying
m = 1

Subproblem 2
Set the factor '(7 + -1m)' equal to zero and attempt to solve:

Simplifying
7 + -1m = 0

Solving
7 + -1m = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1m = 0 + -7
-1m = 0 + -7

Combine like terms: 0 + -7 = -7
-1m = -7

Divide each side by '-1'.
m = 7

Simplifying
m = 7
Solution
m = {1, 7}

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