2m+5m(m-6)=3m+14

Solution for 2m+5m(m-6)=3m+14 equation:

Simplifying
2m + 5m(m + -6) = 3m + 14

Reorder the terms:
2m + 5m(-6 + m) = 3m + 14
2m + (-6 * 5m + m * 5m) = 3m + 14
2m + (-30m + 5m2) = 3m + 14

Combine like terms: 2m + -30m = -28m
-28m + 5m2 = 3m + 14

Reorder the terms:
-28m + 5m2 = 14 + 3m

Solving
-28m + 5m2 = 14 + 3m

Solving for variable 'm'.

Reorder the terms:
-14 + -28m + -3m + 5m2 = 14 + 3m + -14 + -3m

Combine like terms: -28m + -3m = -31m
-14 + -31m + 5m2 = 14 + 3m + -14 + -3m

Reorder the terms:
-14 + -31m + 5m2 = 14 + -14 + 3m + -3m

Combine like terms: 14 + -14 = 0
-14 + -31m + 5m2 = 0 + 3m + -3m
-14 + -31m + 5m2 = 3m + -3m

Combine like terms: 3m + -3m = 0
-14 + -31m + 5m2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-2.8 + -6.2m + m2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -6.2m + 2.8 + m2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -6.2m + m2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -6.2m + m2 = 0 + 2.8
-6.2m + m2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-6.2m + m2 = 2.8

The m term is -6.2m.  Take half its coefficient (-3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
-6.2m + 9.61 + m2 = 2.8 + 9.61

Reorder the terms:
9.61 + -6.2m + m2 = 2.8 + 9.61

Combine like terms: 2.8 + 9.61 = 12.41
9.61 + -6.2m + m2 = 12.41

Factor a perfect square on the left side:
(m + -3.1)(m + -3.1) = 12.41

Calculate the square root of the right side: 3.522782991

Break this problem into two subproblems by setting 
(m + -3.1) equal to 3.522782991 and -3.522782991.

Subproblem 1
m + -3.1 = 3.522782991

Simplifying
m + -3.1 = 3.522782991

Reorder the terms:
-3.1 + m = 3.522782991

Solving
-3.1 + m = 3.522782991

Solving for variable 'm'.

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

Add '3.1' to each side of the equation.
-3.1 + 3.1 + m = 3.522782991 + 3.1

Combine like terms: -3.1 + 3.1 = 0.0
0.0 + m = 3.522782991 + 3.1
m = 3.522782991 + 3.1

Combine like terms: 3.522782991 + 3.1 = 6.622782991
m = 6.622782991

Simplifying
m = 6.622782991

Subproblem 2
m + -3.1 = -3.522782991

Simplifying
m + -3.1 = -3.522782991

Reorder the terms:
-3.1 + m = -3.522782991

Solving
-3.1 + m = -3.522782991

Solving for variable 'm'.

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

Add '3.1' to each side of the equation.
-3.1 + 3.1 + m = -3.522782991 + 3.1

Combine like terms: -3.1 + 3.1 = 0.0
0.0 + m = -3.522782991 + 3.1
m = -3.522782991 + 3.1

Combine like terms: -3.522782991 + 3.1 = -0.422782991
m = -0.422782991

Simplifying
m = -0.422782991

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {6.622782991, -0.422782991}