(m+2)(m+3)=(m-3)(m+2)

Solution for (m+2)(m+3)=(m-3)(m+2) equation:

Simplifying
(m + 2)(m + 3) = (m + -3)(m + 2)

Reorder the terms:
(2 + m)(m + 3) = (m + -3)(m + 2)

Reorder the terms:
(2 + m)(3 + m) = (m + -3)(m + 2)

Multiply (2 + m) * (3 + m)
(2(3 + m) + m(3 + m)) = (m + -3)(m + 2)
((3 * 2 + m * 2) + m(3 + m)) = (m + -3)(m + 2)
((6 + 2m) + m(3 + m)) = (m + -3)(m + 2)
(6 + 2m + (3 * m + m * m)) = (m + -3)(m + 2)
(6 + 2m + (3m + m2)) = (m + -3)(m + 2)

Combine like terms: 2m + 3m = 5m
(6 + 5m + m2) = (m + -3)(m + 2)

Reorder the terms:
6 + 5m + m2 = (-3 + m)(m + 2)

Reorder the terms:
6 + 5m + m2 = (-3 + m)(2 + m)

Multiply (-3 + m) * (2 + m)
6 + 5m + m2 = (-3(2 + m) + m(2 + m))
6 + 5m + m2 = ((2 * -3 + m * -3) + m(2 + m))
6 + 5m + m2 = ((-6 + -3m) + m(2 + m))
6 + 5m + m2 = (-6 + -3m + (2 * m + m * m))
6 + 5m + m2 = (-6 + -3m + (2m + m2))

Combine like terms: -3m + 2m = -1m
6 + 5m + m2 = (-6 + -1m + m2)

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

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

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

Solving
6 + 5m = -6 + -1m

Solving for variable 'm'.

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

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

Combine like terms: 5m + m = 6m
6 + 6m = -6 + -1m + m

Combine like terms: -1m + m = 0
6 + 6m = -6 + 0
6 + 6m = -6

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

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

Combine like terms: -6 + -6 = -12
6m = -12

Divide each side by '6'.
m = -2

Simplifying
m = -2