2m^2+3m+13=7m+1

Solution for 2m^2+3m+13=7m+1 equation:

Simplifying
2m2 + 3m + 13 = 7m + 1

Reorder the terms:
13 + 3m + 2m2 = 7m + 1

Reorder the terms:
13 + 3m + 2m2 = 1 + 7m

Solving
13 + 3m + 2m2 = 1 + 7m

Solving for variable 'm'.

Reorder the terms:
13 + -1 + 3m + -7m + 2m2 = 1 + 7m + -1 + -7m

Combine like terms: 13 + -1 = 12
12 + 3m + -7m + 2m2 = 1 + 7m + -1 + -7m

Combine like terms: 3m + -7m = -4m
12 + -4m + 2m2 = 1 + 7m + -1 + -7m

Reorder the terms:
12 + -4m + 2m2 = 1 + -1 + 7m + -7m

Combine like terms: 1 + -1 = 0
12 + -4m + 2m2 = 0 + 7m + -7m
12 + -4m + 2m2 = 7m + -7m

Combine like terms: 7m + -7m = 0
12 + -4m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -2m + m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -2m + m2)' equal to zero and attempt to solve:

Simplifying
6 + -2m + m2 = 0

Solving
6 + -2m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -2m + -6 + m2 = 0 + -6

Reorder the terms:
6 + -6 + -2m + m2 = 0 + -6

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

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

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = -6 + 1

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

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

Factor a perfect square on the left side:
(m + -1)(m + -1) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.