(3m+2)(m-1)-13=2m(2-m)

Solution for (3m+2)(m-1)-13=2m(2-m) equation:

Simplifying
(3m + 2)(m + -1) + -13 = 2m(2 + -1m)

Reorder the terms:
(2 + 3m)(m + -1) + -13 = 2m(2 + -1m)

Reorder the terms:
(2 + 3m)(-1 + m) + -13 = 2m(2 + -1m)

Multiply (2 + 3m) * (-1 + m)
(2(-1 + m) + 3m * (-1 + m)) + -13 = 2m(2 + -1m)
((-1 * 2 + m * 2) + 3m * (-1 + m)) + -13 = 2m(2 + -1m)
((-2 + 2m) + 3m * (-1 + m)) + -13 = 2m(2 + -1m)
(-2 + 2m + (-1 * 3m + m * 3m)) + -13 = 2m(2 + -1m)
(-2 + 2m + (-3m + 3m2)) + -13 = 2m(2 + -1m)

Combine like terms: 2m + -3m = -1m
(-2 + -1m + 3m2) + -13 = 2m(2 + -1m)

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

Combine like terms: -2 + -13 = -15
-15 + -1m + 3m2 = 2m(2 + -1m)
-15 + -1m + 3m2 = (2 * 2m + -1m * 2m)
-15 + -1m + 3m2 = (4m + -2m2)

Solving
-15 + -1m + 3m2 = 4m + -2m2

Solving for variable 'm'.

Reorder the terms:
-15 + -1m + -4m + 3m2 + 2m2 = 4m + -2m2 + -4m + 2m2

Combine like terms: -1m + -4m = -5m
-15 + -5m + 3m2 + 2m2 = 4m + -2m2 + -4m + 2m2

Combine like terms: 3m2 + 2m2 = 5m2
-15 + -5m + 5m2 = 4m + -2m2 + -4m + 2m2

Reorder the terms:
-15 + -5m + 5m2 = 4m + -4m + -2m2 + 2m2

Combine like terms: 4m + -4m = 0
-15 + -5m + 5m2 = 0 + -2m2 + 2m2
-15 + -5m + 5m2 = -2m2 + 2m2

Combine like terms: -2m2 + 2m2 = 0
-15 + -5m + 5m2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -1m + m2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + -1m + m2)' equal to zero and attempt to solve:

Simplifying
-3 + -1m + m2 = 0

Solving
-3 + -1m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1m + 3 + m2 = 0 + 3

Reorder the terms:
-3 + 3 + -1m + m2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1m + m2 = 0 + 3
-1m + m2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1m + m2 = 3

The m term is -1m.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1m + 0.25 + m2 = 3 + 0.25

Reorder the terms:
0.25 + -1m + m2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1m + m2 = 3.25

Factor a perfect square on the left side:
(m + -0.5)(m + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(m + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
m + -0.5 = 1.802775638

Simplifying
m + -0.5 = 1.802775638

Reorder the terms:
-0.5 + m = 1.802775638

Solving
-0.5 + m = 1.802775638

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = 1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = 1.802775638 + 0.5
m = 1.802775638 + 0.5

Combine like terms: 1.802775638 + 0.5 = 2.302775638
m = 2.302775638

Simplifying
m = 2.302775638

Subproblem 2
m + -0.5 = -1.802775638

Simplifying
m + -0.5 = -1.802775638

Reorder the terms:
-0.5 + m = -1.802775638

Solving
-0.5 + m = -1.802775638

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = -1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = -1.802775638 + 0.5
m = -1.802775638 + 0.5

Combine like terms: -1.802775638 + 0.5 = -1.302775638
m = -1.302775638

Simplifying
m = -1.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.302775638, -1.302775638}
Solution
m = {2.302775638, -1.302775638}