[m+2][m+3]=[m+2][m-2]

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Solution for [m+2][m+3]=[m+2][m-2] equation: 


Simplifying
[m + 2][m + 3] = [m + 2][m + -2]

Reorder the terms:
[2 + m][m + 3] = [m + 2][m + -2]

Reorder the terms:
[2 + m][3 + m] = [m + 2][m + -2]

Multiply [2 + m] * [3 + m]
[2[3 + m] + m[3 + m]] = [m + 2][m + -2]
[[3 * 2 + m * 2] + m[3 + m]] = [m + 2][m + -2]
[[6 + 2m] + m[3 + m]] = [m + 2][m + -2]
[6 + 2m + [3 * m + m * m]] = [m + 2][m + -2]
[6 + 2m + [3m + m2]] = [m + 2][m + -2]

Combine like terms: 2m + 3m = 5m
[6 + 5m + m2] = [m + 2][m + -2]

Reorder the terms:
6 + 5m + m2 = [2 + m][m + -2]

Reorder the terms:
6 + 5m + m2 = [2 + m][-2 + m]

Multiply [2 + m] * [-2 + m]
6 + 5m + m2 = [2[-2 + m] + m[-2 + m]]
6 + 5m + m2 = [[-2 * 2 + m * 2] + m[-2 + m]]
6 + 5m + m2 = [[-4 + 2m] + m[-2 + m]]
6 + 5m + m2 = [-4 + 2m + [-2 * m + m * m]]
6 + 5m + m2 = [-4 + 2m + [-2m + m2]]

Combine like terms: 2m + -2m = 0
6 + 5m + m2 = [-4 + 0 + m2]
6 + 5m + m2 = [-4 + m2]

Add '-1m2' to each side of the equation.
6 + 5m + m2 + -1m2 = -4 + m2 + -1m2

Combine like terms: m2 + -1m2 = 0
6 + 5m + 0 = -4 + m2 + -1m2
6 + 5m = -4 + m2 + -1m2

Combine like terms: m2 + -1m2 = 0
6 + 5m = -4 + 0
6 + 5m = -4

Solving
6 + 5m = -4

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + 5m = -4 + -6

Combine like terms: 6 + -6 = 0
0 + 5m = -4 + -6
5m = -4 + -6

Combine like terms: -4 + -6 = -10
5m = -10

Divide each side by '5'.
m = -2

Simplifying
m = -2

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