(2m)(m-3)=7

Solution for (2m)(m-3)=7 equation:

Simplifying
(2m)(m + -3) = 7

Remove parenthesis around (2m)
2m(m + -3) = 7

Reorder the terms:
2m(-3 + m) = 7
(-3 * 2m + m * 2m) = 7
(-6m + 2m2) = 7

Solving
-6m + 2m2 = 7

Solving for variable 'm'.

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

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

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

Divide each side by '2'.
-3.5 + -3m + m2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -3m + 3.5 + m2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -3m + m2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -3m + m2 = 0 + 3.5
-3m + m2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-3m + m2 = 3.5

The m term is -3m.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3m + 2.25 + m2 = 3.5 + 2.25

Reorder the terms:
2.25 + -3m + m2 = 3.5 + 2.25

Combine like terms: 3.5 + 2.25 = 5.75
2.25 + -3m + m2 = 5.75

Factor a perfect square on the left side:
(m + -1.5)(m + -1.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(m + -1.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
m + -1.5 = 2.397915762

Simplifying
m + -1.5 = 2.397915762

Reorder the terms:
-1.5 + m = 2.397915762

Solving
-1.5 + m = 2.397915762

Solving for variable 'm'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + m = 2.397915762 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = 2.397915762 + 1.5
m = 2.397915762 + 1.5

Combine like terms: 2.397915762 + 1.5 = 3.897915762
m = 3.897915762

Simplifying
m = 3.897915762

Subproblem 2
m + -1.5 = -2.397915762

Simplifying
m + -1.5 = -2.397915762

Reorder the terms:
-1.5 + m = -2.397915762

Solving
-1.5 + m = -2.397915762

Solving for variable 'm'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + m = -2.397915762 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = -2.397915762 + 1.5
m = -2.397915762 + 1.5

Combine like terms: -2.397915762 + 1.5 = -0.897915762
m = -0.897915762

Simplifying
m = -0.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.897915762, -0.897915762}