10m(m+3)=13m-3

Solution for 10m(m+3)=13m-3 equation:

Simplifying
10m(m + 3) = 13m + -3

Reorder the terms:
10m(3 + m) = 13m + -3
(3 * 10m + m * 10m) = 13m + -3
(30m + 10m2) = 13m + -3

Reorder the terms:
30m + 10m2 = -3 + 13m

Solving
30m + 10m2 = -3 + 13m

Solving for variable 'm'.

Reorder the terms:
3 + 30m + -13m + 10m2 = -3 + 13m + 3 + -13m

Combine like terms: 30m + -13m = 17m
3 + 17m + 10m2 = -3 + 13m + 3 + -13m

Reorder the terms:
3 + 17m + 10m2 = -3 + 3 + 13m + -13m

Combine like terms: -3 + 3 = 0
3 + 17m + 10m2 = 0 + 13m + -13m
3 + 17m + 10m2 = 13m + -13m

Combine like terms: 13m + -13m = 0
3 + 17m + 10m2 = 0

Factor a trinomial.
(3 + 2m)(1 + 5m) = 0

Subproblem 1
Set the factor '(3 + 2m)' equal to zero and attempt to solve:

Simplifying
3 + 2m = 0

Solving
3 + 2m = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2m = 0 + -3

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

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

Divide each side by '2'.
m = -1.5

Simplifying
m = -1.5
Subproblem 2
Set the factor '(1 + 5m)' equal to zero and attempt to solve:

Simplifying
1 + 5m = 0

Solving
1 + 5m = 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 + 5m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5m = 0 + -1
5m = 0 + -1

Combine like terms: 0 + -1 = -1
5m = -1

Divide each side by '5'.
m = -0.2

Simplifying
m = -0.2
Solution
m = {-1.5, -0.2}