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

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

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

Reorder the terms:
2m(2 + -1m) = 3(2m + 1)
(2 * 2m + -1m * 2m) = 3(2m + 1)
(4m + -2m2) = 3(2m + 1)

Reorder the terms:
4m + -2m2 = 3(1 + 2m)
4m + -2m2 = (1 * 3 + 2m * 3)
4m + -2m2 = (3 + 6m)

Solving
4m + -2m2 = 3 + 6m

Solving for variable 'm'.

Reorder the terms:
-3 + 4m + -6m + -2m2 = 3 + 6m + -3 + -6m

Combine like terms: 4m + -6m = -2m
-3 + -2m + -2m2 = 3 + 6m + -3 + -6m

Reorder the terms:
-3 + -2m + -2m2 = 3 + -3 + 6m + -6m

Combine like terms: 3 + -3 = 0
-3 + -2m + -2m2 = 0 + 6m + -6m
-3 + -2m + -2m2 = 6m + -6m

Combine like terms: 6m + -6m = 0
-3 + -2m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 2m + 2m2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 2m + 2m2)' equal to zero and attempt to solve:

Simplifying
3 + 2m + 2m2 = 0

Solving
3 + 2m + 2m2 = 0

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

Divide each side by '2'.
1.5 + m + m2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + m + -1.5 + m2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + m + m2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m + m2 = 0 + -1.5
m + m2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
m + m2 = -1.5

The m term is m.  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.
 + 0.25 + m2 = -1.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + m2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
1.25 + m2 = -1.25

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.