2m+5(3-m(m+1))=5(2-m)+12

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Solution for 2m+5(3-m(m+1))=5(2-m)+12 equation: 


Simplifying
2m + 5(3 + -1m(m + 1)) = 5(2 + -1m) + 12

Reorder the terms:
2m + 5(3 + -1m(1 + m)) = 5(2 + -1m) + 12
2m + 5(3 + (1 * -1m + m * -1m)) = 5(2 + -1m) + 12
2m + 5(3 + (-1m + -1m2)) = 5(2 + -1m) + 12
2m + (3 * 5 + -1m * 5 + -1m2 * 5) = 5(2 + -1m) + 12
2m + (15 + -5m + -5m2) = 5(2 + -1m) + 12

Reorder the terms:
15 + 2m + -5m + -5m2 = 5(2 + -1m) + 12

Combine like terms: 2m + -5m = -3m
15 + -3m + -5m2 = 5(2 + -1m) + 12
15 + -3m + -5m2 = (2 * 5 + -1m * 5) + 12
15 + -3m + -5m2 = (10 + -5m) + 12

Reorder the terms:
15 + -3m + -5m2 = 10 + 12 + -5m

Combine like terms: 10 + 12 = 22
15 + -3m + -5m2 = 22 + -5m

Solving
15 + -3m + -5m2 = 22 + -5m

Solving for variable 'm'.

Reorder the terms:
15 + -22 + -3m + 5m + -5m2 = 22 + -5m + -22 + 5m

Combine like terms: 15 + -22 = -7
-7 + -3m + 5m + -5m2 = 22 + -5m + -22 + 5m

Combine like terms: -3m + 5m = 2m
-7 + 2m + -5m2 = 22 + -5m + -22 + 5m

Reorder the terms:
-7 + 2m + -5m2 = 22 + -22 + -5m + 5m

Combine like terms: 22 + -22 = 0
-7 + 2m + -5m2 = 0 + -5m + 5m
-7 + 2m + -5m2 = -5m + 5m

Combine like terms: -5m + 5m = 0
-7 + 2m + -5m2 = 0

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

Divide each side by '-5'.
1.4 + -0.4m + m2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + -0.4m + -1.4 + m2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + -0.4m + m2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + -0.4m + m2 = 0 + -1.4
-0.4m + m2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
-0.4m + m2 = -1.4

The m term is -0.4m.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4m + 0.04 + m2 = -1.4 + 0.04

Reorder the terms:
0.04 + -0.4m + m2 = -1.4 + 0.04

Combine like terms: -1.4 + 0.04 = -1.36
0.04 + -0.4m + m2 = -1.36

Factor a perfect square on the left side:
(m + -0.2)(m + -0.2) = -1.36

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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