2m^2+6m-28=m-3

Solution for 2m^2+6m-28=m-3 equation:

Simplifying
2m2 + 6m + -28 = m + -3

Reorder the terms:
-28 + 6m + 2m2 = m + -3

Reorder the terms:
-28 + 6m + 2m2 = -3 + m

Solving
-28 + 6m + 2m2 = -3 + m

Solving for variable 'm'.

Reorder the terms:
-28 + 3 + 6m + -1m + 2m2 = -3 + m + 3 + -1m

Combine like terms: -28 + 3 = -25
-25 + 6m + -1m + 2m2 = -3 + m + 3 + -1m

Combine like terms: 6m + -1m = 5m
-25 + 5m + 2m2 = -3 + m + 3 + -1m

Reorder the terms:
-25 + 5m + 2m2 = -3 + 3 + m + -1m

Combine like terms: -3 + 3 = 0
-25 + 5m + 2m2 = 0 + m + -1m
-25 + 5m + 2m2 = m + -1m

Combine like terms: m + -1m = 0
-25 + 5m + 2m2 = 0

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

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

Simplifying
-5 + -1m = 0

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

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

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

Divide each side by '-1'.
m = -5

Simplifying
m = -5
Subproblem 2
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
Solution
m = {-5, 2.5}