3m^2+5=m^2-7m-1

Solution for 3m^2+5=m^2-7m-1 equation:

Simplifying
3m2 + 5 = m2 + -7m + -1

Reorder the terms:
5 + 3m2 = m2 + -7m + -1

Reorder the terms:
5 + 3m2 = -1 + -7m + m2

Solving
5 + 3m2 = -1 + -7m + m2

Solving for variable 'm'.

Reorder the terms:
5 + 1 + 7m + 3m2 + -1m2 = -1 + -7m + m2 + 1 + 7m + -1m2

Combine like terms: 5 + 1 = 6
6 + 7m + 3m2 + -1m2 = -1 + -7m + m2 + 1 + 7m + -1m2

Combine like terms: 3m2 + -1m2 = 2m2
6 + 7m + 2m2 = -1 + -7m + m2 + 1 + 7m + -1m2

Reorder the terms:
6 + 7m + 2m2 = -1 + 1 + -7m + 7m + m2 + -1m2

Combine like terms: -1 + 1 = 0
6 + 7m + 2m2 = 0 + -7m + 7m + m2 + -1m2
6 + 7m + 2m2 = -7m + 7m + m2 + -1m2

Combine like terms: -7m + 7m = 0
6 + 7m + 2m2 = 0 + m2 + -1m2
6 + 7m + 2m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
6 + 7m + 2m2 = 0

Factor a trinomial.
(2 + m)(3 + 2m) = 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 '(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
Solution
m = {-2, -1.5}