2m(m-2)=m(m+3)-6

Solution for 2m(m-2)=m(m+3)-6 equation:

Simplifying
2m(m + -2) = m(m + 3) + -6

Reorder the terms:
2m(-2 + m) = m(m + 3) + -6
(-2 * 2m + m * 2m) = m(m + 3) + -6
(-4m + 2m2) = m(m + 3) + -6

Reorder the terms:
-4m + 2m2 = m(3 + m) + -6
-4m + 2m2 = (3 * m + m * m) + -6
-4m + 2m2 = (3m + m2) + -6

Reorder the terms:
-4m + 2m2 = -6 + 3m + m2

Solving
-4m + 2m2 = -6 + 3m + m2

Solving for variable 'm'.

Reorder the terms:
6 + -4m + -3m + 2m2 + -1m2 = -6 + 3m + m2 + 6 + -3m + -1m2

Combine like terms: -4m + -3m = -7m
6 + -7m + 2m2 + -1m2 = -6 + 3m + m2 + 6 + -3m + -1m2

Combine like terms: 2m2 + -1m2 = 1m2
6 + -7m + 1m2 = -6 + 3m + m2 + 6 + -3m + -1m2

Reorder the terms:
6 + -7m + 1m2 = -6 + 6 + 3m + -3m + m2 + -1m2

Combine like terms: -6 + 6 = 0
6 + -7m + 1m2 = 0 + 3m + -3m + m2 + -1m2
6 + -7m + 1m2 = 3m + -3m + m2 + -1m2

Combine like terms: 3m + -3m = 0
6 + -7m + 1m2 = 0 + m2 + -1m2
6 + -7m + 1m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
6 + -7m + 1m2 = 0

Factor a trinomial.
(1 + -1m)(6 + -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 '(6 + -1m)' equal to zero and attempt to solve:

Simplifying
6 + -1m = 0

Solving
6 + -1m = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1m = 0 + -6

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

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

Divide each side by '-1'.
m = 6

Simplifying
m = 6
Solution
m = {1, 6}