7m-2=m(4+m)

Solution for 7m-2=m(4+m) equation:

Simplifying
7m + -2 = m(4 + m)

Reorder the terms:
-2 + 7m = m(4 + m)
-2 + 7m = (4 * m + m * m)
-2 + 7m = (4m + m2)

Solving
-2 + 7m = 4m + m2

Solving for variable 'm'.

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

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

Combine like terms: 4m + -4m = 0
-2 + 3m + -1m2 = 0 + m2 + -1m2
-2 + 3m + -1m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
-2 + 3m + -1m2 = 0

Factor a trinomial.
(-2 + m)(1 + -1m) = 0

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

Simplifying
-2 + m = 0

Solving
-2 + m = 0

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

Add '2' to each side of the equation.
-2 + 2 + m = 0 + 2

Combine like terms: -2 + 2 = 0
0 + m = 0 + 2
m = 0 + 2

Combine like terms: 0 + 2 = 2
m = 2

Simplifying
m = 2
Subproblem 2
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
Solution
m = {2, 1}