10m(m+2)+2(m+1)=m

Solution for 10m(m+2)+2(m+1)=m equation:

Simplifying
10m(m + 2) + 2(m + 1) = m

Reorder the terms:
10m(2 + m) + 2(m + 1) = m
(2 * 10m + m * 10m) + 2(m + 1) = m
(20m + 10m2) + 2(m + 1) = m

Reorder the terms:
20m + 10m2 + 2(1 + m) = m
20m + 10m2 + (1 * 2 + m * 2) = m
20m + 10m2 + (2 + 2m) = m

Reorder the terms:
2 + 20m + 2m + 10m2 = m

Combine like terms: 20m + 2m = 22m
2 + 22m + 10m2 = m

Solving
2 + 22m + 10m2 = m

Solving for variable 'm'.

Reorder the terms:
2 + 22m + -1m + 10m2 = m + -1m

Combine like terms: 22m + -1m = 21m
2 + 21m + 10m2 = m + -1m

Combine like terms: m + -1m = 0
2 + 21m + 10m2 = 0

Factor a trinomial.
(2 + m)(1 + 10m) = 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 + 10m)' equal to zero and attempt to solve:

Simplifying
1 + 10m = 0

Solving
1 + 10m = 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 + 10m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10m = 0 + -1
10m = 0 + -1

Combine like terms: 0 + -1 = -1
10m = -1

Divide each side by '10'.
m = -0.1

Simplifying
m = -0.1
Solution
m = {-2, -0.1}