(m-3)(m-2)=(m+4)(m+5)

Solution for (m-3)(m-2)=(m+4)(m+5) equation:

Simplifying
(m + -3)(m + -2) = (m + 4)(m + 5)

Reorder the terms:
(-3 + m)(m + -2) = (m + 4)(m + 5)

Reorder the terms:
(-3 + m)(-2 + m) = (m + 4)(m + 5)

Multiply (-3 + m) * (-2 + m)
(-3(-2 + m) + m(-2 + m)) = (m + 4)(m + 5)
((-2 * -3 + m * -3) + m(-2 + m)) = (m + 4)(m + 5)
((6 + -3m) + m(-2 + m)) = (m + 4)(m + 5)
(6 + -3m + (-2 * m + m * m)) = (m + 4)(m + 5)
(6 + -3m + (-2m + m2)) = (m + 4)(m + 5)

Combine like terms: -3m + -2m = -5m
(6 + -5m + m2) = (m + 4)(m + 5)

Reorder the terms:
6 + -5m + m2 = (4 + m)(m + 5)

Reorder the terms:
6 + -5m + m2 = (4 + m)(5 + m)

Multiply (4 + m) * (5 + m)
6 + -5m + m2 = (4(5 + m) + m(5 + m))
6 + -5m + m2 = ((5 * 4 + m * 4) + m(5 + m))
6 + -5m + m2 = ((20 + 4m) + m(5 + m))
6 + -5m + m2 = (20 + 4m + (5 * m + m * m))
6 + -5m + m2 = (20 + 4m + (5m + m2))

Combine like terms: 4m + 5m = 9m
6 + -5m + m2 = (20 + 9m + m2)

Add '-1m2' to each side of the equation.
6 + -5m + m2 + -1m2 = 20 + 9m + m2 + -1m2

Combine like terms: m2 + -1m2 = 0
6 + -5m + 0 = 20 + 9m + m2 + -1m2
6 + -5m = 20 + 9m + m2 + -1m2

Combine like terms: m2 + -1m2 = 0
6 + -5m = 20 + 9m + 0
6 + -5m = 20 + 9m

Solving
6 + -5m = 20 + 9m

Solving for variable 'm'.

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

Add '-9m' to each side of the equation.
6 + -5m + -9m = 20 + 9m + -9m

Combine like terms: -5m + -9m = -14m
6 + -14m = 20 + 9m + -9m

Combine like terms: 9m + -9m = 0
6 + -14m = 20 + 0
6 + -14m = 20

Add '-6' to each side of the equation.
6 + -6 + -14m = 20 + -6

Combine like terms: 6 + -6 = 0
0 + -14m = 20 + -6
-14m = 20 + -6

Combine like terms: 20 + -6 = 14
-14m = 14

Divide each side by '-14'.
m = -1

Simplifying
m = -1