-6+2m(m+2)=5(5-5m)

Solution for -6+2m(m+2)=5(5-5m) equation:

Simplifying
-6 + 2m(m + 2) = 5(5 + -5m)

Reorder the terms:
-6 + 2m(2 + m) = 5(5 + -5m)
-6 + (2 * 2m + m * 2m) = 5(5 + -5m)
-6 + (4m + 2m2) = 5(5 + -5m)
-6 + 4m + 2m2 = (5 * 5 + -5m * 5)
-6 + 4m + 2m2 = (25 + -25m)

Solving
-6 + 4m + 2m2 = 25 + -25m

Solving for variable 'm'.

Reorder the terms:
-6 + -25 + 4m + 25m + 2m2 = 25 + -25m + -25 + 25m

Combine like terms: -6 + -25 = -31
-31 + 4m + 25m + 2m2 = 25 + -25m + -25 + 25m

Combine like terms: 4m + 25m = 29m
-31 + 29m + 2m2 = 25 + -25m + -25 + 25m

Reorder the terms:
-31 + 29m + 2m2 = 25 + -25 + -25m + 25m

Combine like terms: 25 + -25 = 0
-31 + 29m + 2m2 = 0 + -25m + 25m
-31 + 29m + 2m2 = -25m + 25m

Combine like terms: -25m + 25m = 0
-31 + 29m + 2m2 = 0

Factor a trinomial.
(-31 + -2m)(1 + -1m) = 0

Subproblem 1
Set the factor '(-31 + -2m)' equal to zero and attempt to solve:

Simplifying
-31 + -2m = 0

Solving
-31 + -2m = 0

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

Add '31' to each side of the equation.
-31 + 31 + -2m = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -2m = 0 + 31
-2m = 0 + 31

Combine like terms: 0 + 31 = 31
-2m = 31

Divide each side by '-2'.
m = -15.5

Simplifying
m = -15.5
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 = {-15.5, 1}