-3m+18-5(m-3)=5m(2m-6)-6m+7

Solution for -3m+18-5(m-3)=5m(2m-6)-6m+7 equation:

Simplifying
-3m + 18 + -5(m + -3) = 5m(2m + -6) + -6m + 7

Reorder the terms:
-3m + 18 + -5(-3 + m) = 5m(2m + -6) + -6m + 7
-3m + 18 + (-3 * -5 + m * -5) = 5m(2m + -6) + -6m + 7
-3m + 18 + (15 + -5m) = 5m(2m + -6) + -6m + 7

Reorder the terms:
18 + 15 + -3m + -5m = 5m(2m + -6) + -6m + 7

Combine like terms: 18 + 15 = 33
33 + -3m + -5m = 5m(2m + -6) + -6m + 7

Combine like terms: -3m + -5m = -8m
33 + -8m = 5m(2m + -6) + -6m + 7

Reorder the terms:
33 + -8m = 5m(-6 + 2m) + -6m + 7
33 + -8m = (-6 * 5m + 2m * 5m) + -6m + 7
33 + -8m = (-30m + 10m2) + -6m + 7

Reorder the terms:
33 + -8m = 7 + -30m + -6m + 10m2

Combine like terms: -30m + -6m = -36m
33 + -8m = 7 + -36m + 10m2

Solving
33 + -8m = 7 + -36m + 10m2

Solving for variable 'm'.

Reorder the terms:
33 + -7 + -8m + 36m + -10m2 = 7 + -36m + 10m2 + -7 + 36m + -10m2

Combine like terms: 33 + -7 = 26
26 + -8m + 36m + -10m2 = 7 + -36m + 10m2 + -7 + 36m + -10m2

Combine like terms: -8m + 36m = 28m
26 + 28m + -10m2 = 7 + -36m + 10m2 + -7 + 36m + -10m2

Reorder the terms:
26 + 28m + -10m2 = 7 + -7 + -36m + 36m + 10m2 + -10m2

Combine like terms: 7 + -7 = 0
26 + 28m + -10m2 = 0 + -36m + 36m + 10m2 + -10m2
26 + 28m + -10m2 = -36m + 36m + 10m2 + -10m2

Combine like terms: -36m + 36m = 0
26 + 28m + -10m2 = 0 + 10m2 + -10m2
26 + 28m + -10m2 = 10m2 + -10m2

Combine like terms: 10m2 + -10m2 = 0
26 + 28m + -10m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 14m + -5m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13 + 14m + -5m2)' equal to zero and attempt to solve:

Simplifying
13 + 14m + -5m2 = 0

Solving
13 + 14m + -5m2 = 0

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

Divide each side by '-5'.
-2.6 + -2.8m + m2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + -2.8m + 2.6 + m2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + -2.8m + m2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + -2.8m + m2 = 0 + 2.6
-2.8m + m2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
-2.8m + m2 = 2.6

The m term is -2.8m.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8m + 1.96 + m2 = 2.6 + 1.96

Reorder the terms:
1.96 + -2.8m + m2 = 2.6 + 1.96

Combine like terms: 2.6 + 1.96 = 4.56
1.96 + -2.8m + m2 = 4.56

Factor a perfect square on the left side:
(m + -1.4)(m + -1.4) = 4.56

Calculate the square root of the right side: 2.13541565

Break this problem into two subproblems by setting 
(m + -1.4) equal to 2.13541565 and -2.13541565.

Subproblem 1
m + -1.4 = 2.13541565

Simplifying
m + -1.4 = 2.13541565

Reorder the terms:
-1.4 + m = 2.13541565

Solving
-1.4 + m = 2.13541565

Solving for variable 'm'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + m = 2.13541565 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + m = 2.13541565 + 1.4
m = 2.13541565 + 1.4

Combine like terms: 2.13541565 + 1.4 = 3.53541565
m = 3.53541565

Simplifying
m = 3.53541565

Subproblem 2
m + -1.4 = -2.13541565

Simplifying
m + -1.4 = -2.13541565

Reorder the terms:
-1.4 + m = -2.13541565

Solving
-1.4 + m = -2.13541565

Solving for variable 'm'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + m = -2.13541565 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + m = -2.13541565 + 1.4
m = -2.13541565 + 1.4

Combine like terms: -2.13541565 + 1.4 = -0.73541565
m = -0.73541565

Simplifying
m = -0.73541565

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.53541565, -0.73541565}
Solution
m = {3.53541565, -0.73541565}