10m(m+4)=7m-20

Solution for 10m(m+4)=7m-20 equation:

Simplifying
10m(m + 4) = 7m + -20

Reorder the terms:
10m(4 + m) = 7m + -20
(4 * 10m + m * 10m) = 7m + -20
(40m + 10m2) = 7m + -20

Reorder the terms:
40m + 10m2 = -20 + 7m

Solving
40m + 10m2 = -20 + 7m

Solving for variable 'm'.

Reorder the terms:
20 + 40m + -7m + 10m2 = -20 + 7m + 20 + -7m

Combine like terms: 40m + -7m = 33m
20 + 33m + 10m2 = -20 + 7m + 20 + -7m

Reorder the terms:
20 + 33m + 10m2 = -20 + 20 + 7m + -7m

Combine like terms: -20 + 20 = 0
20 + 33m + 10m2 = 0 + 7m + -7m
20 + 33m + 10m2 = 7m + -7m

Combine like terms: 7m + -7m = 0
20 + 33m + 10m2 = 0

Factor a trinomial.
(5 + 2m)(4 + 5m) = 0

Subproblem 1
Set the factor '(5 + 2m)' equal to zero and attempt to solve:

Simplifying
5 + 2m = 0

Solving
5 + 2m = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2m = 0 + -5
2m = 0 + -5

Combine like terms: 0 + -5 = -5
2m = -5

Divide each side by '2'.
m = -2.5

Simplifying
m = -2.5
Subproblem 2
Set the factor '(4 + 5m)' equal to zero and attempt to solve:

Simplifying
4 + 5m = 0

Solving
4 + 5m = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5m = 0 + -4
5m = 0 + -4

Combine like terms: 0 + -4 = -4
5m = -4

Divide each side by '5'.
m = -0.8

Simplifying
m = -0.8
Solution
m = {-2.5, -0.8}