7(m-5)=15(3-m)2m

Solution for 7(m-5)=15(3-m)2m equation:

Simplifying
7(m + -5) = 15(3 + -1m) * 2m

Reorder the terms:
7(-5 + m) = 15(3 + -1m) * 2m
(-5 * 7 + m * 7) = 15(3 + -1m) * 2m
(-35 + 7m) = 15(3 + -1m) * 2m

Reorder the terms for easier multiplication:
-35 + 7m = 15 * 2m(3 + -1m)

Multiply 15 * 2
-35 + 7m = 30m(3 + -1m)
-35 + 7m = (3 * 30m + -1m * 30m)
-35 + 7m = (90m + -30m2)

Solving
-35 + 7m = 90m + -30m2

Solving for variable 'm'.

Combine like terms: 7m + -90m = -83m
-35 + -83m + 30m2 = 90m + -30m2 + -90m + 30m2

Reorder the terms:
-35 + -83m + 30m2 = 90m + -90m + -30m2 + 30m2

Combine like terms: 90m + -90m = 0
-35 + -83m + 30m2 = 0 + -30m2 + 30m2
-35 + -83m + 30m2 = -30m2 + 30m2

Combine like terms: -30m2 + 30m2 = 0
-35 + -83m + 30m2 = 0

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

Divide each side by '30'.
-1.166666667 + -2.766666667m + m2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + -2.766666667m + 1.166666667 + m2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + -2.766666667m + m2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + -2.766666667m + m2 = 0 + 1.166666667
-2.766666667m + m2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
-2.766666667m + m2 = 1.166666667

The m term is -2.766666667m.  Take half its coefficient (-1.383333334).
Square it (1.913611113) and add it to both sides.

Add '1.913611113' to each side of the equation.
-2.766666667m + 1.913611113 + m2 = 1.166666667 + 1.913611113

Reorder the terms:
1.913611113 + -2.766666667m + m2 = 1.166666667 + 1.913611113

Combine like terms: 1.166666667 + 1.913611113 = 3.08027778
1.913611113 + -2.766666667m + m2 = 3.08027778

Factor a perfect square on the left side:
(m + -1.383333334)(m + -1.383333334) = 3.08027778

Calculate the square root of the right side: 1.755072016

Break this problem into two subproblems by setting 
(m + -1.383333334) equal to 1.755072016 and -1.755072016.

Subproblem 1
m + -1.383333334 = 1.755072016

Simplifying
m + -1.383333334 = 1.755072016

Reorder the terms:
-1.383333334 + m = 1.755072016

Solving
-1.383333334 + m = 1.755072016

Solving for variable 'm'.

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

Add '1.383333334' to each side of the equation.
-1.383333334 + 1.383333334 + m = 1.755072016 + 1.383333334

Combine like terms: -1.383333334 + 1.383333334 = 0.000000000
0.000000000 + m = 1.755072016 + 1.383333334
m = 1.755072016 + 1.383333334

Combine like terms: 1.755072016 + 1.383333334 = 3.13840535
m = 3.13840535

Simplifying
m = 3.13840535

Subproblem 2
m + -1.383333334 = -1.755072016

Simplifying
m + -1.383333334 = -1.755072016

Reorder the terms:
-1.383333334 + m = -1.755072016

Solving
-1.383333334 + m = -1.755072016

Solving for variable 'm'.

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

Add '1.383333334' to each side of the equation.
-1.383333334 + 1.383333334 + m = -1.755072016 + 1.383333334

Combine like terms: -1.383333334 + 1.383333334 = 0.000000000
0.000000000 + m = -1.755072016 + 1.383333334
m = -1.755072016 + 1.383333334

Combine like terms: -1.755072016 + 1.383333334 = -0.371738682
m = -0.371738682

Simplifying
m = -0.371738682

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.13840535, -0.371738682}