4[5(m+1)+2(m+3n)+1]+5[4+2(2m+n)]=

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Solution for 4[5(m+1)+2(m+3n)+1]+5[4+2(2m+n)]= equation: 


Simplifying
4[5(m + 1) + 2(m + 3n) + 1] + 5[4 + 2(2m + n)] = 0

Reorder the terms:
4[5(1 + m) + 2(m + 3n) + 1] + 5[4 + 2(2m + n)] = 0
4[(1 * 5 + m * 5) + 2(m + 3n) + 1] + 5[4 + 2(2m + n)] = 0
4[(5 + 5m) + 2(m + 3n) + 1] + 5[4 + 2(2m + n)] = 0
4[5 + 5m + (m * 2 + 3n * 2) + 1] + 5[4 + 2(2m + n)] = 0
4[5 + 5m + (2m + 6n) + 1] + 5[4 + 2(2m + n)] = 0

Reorder the terms:
4[5 + 1 + 5m + 2m + 6n] + 5[4 + 2(2m + n)] = 0

Combine like terms: 5 + 1 = 6
4[6 + 5m + 2m + 6n] + 5[4 + 2(2m + n)] = 0

Combine like terms: 5m + 2m = 7m
4[6 + 7m + 6n] + 5[4 + 2(2m + n)] = 0
[6 * 4 + 7m * 4 + 6n * 4] + 5[4 + 2(2m + n)] = 0
[24 + 28m + 24n] + 5[4 + 2(2m + n)] = 0
24 + 28m + 24n + 5[4 + (2m * 2 + n * 2)] = 0
24 + 28m + 24n + 5[4 + (4m + 2n)] = 0
24 + 28m + 24n + [4 * 5 + 4m * 5 + 2n * 5] = 0
24 + 28m + 24n + [20 + 20m + 10n] = 0

Reorder the terms:
24 + 20 + 28m + 20m + 24n + 10n = 0

Combine like terms: 24 + 20 = 44
44 + 28m + 20m + 24n + 10n = 0

Combine like terms: 28m + 20m = 48m
44 + 48m + 24n + 10n = 0

Combine like terms: 24n + 10n = 34n
44 + 48m + 34n = 0

Solving
44 + 48m + 34n = 0

Solving for variable 'm'.

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

Add '-44' to each side of the equation.
44 + 48m + -44 + 34n = 0 + -44

Reorder the terms:
44 + -44 + 48m + 34n = 0 + -44

Combine like terms: 44 + -44 = 0
0 + 48m + 34n = 0 + -44
48m + 34n = 0 + -44

Combine like terms: 0 + -44 = -44
48m + 34n = -44

Add '-34n' to each side of the equation.
48m + 34n + -34n = -44 + -34n

Combine like terms: 34n + -34n = 0
48m + 0 = -44 + -34n
48m = -44 + -34n

Divide each side by '48'.
m = -0.9166666667 + -0.7083333333n

Simplifying
m = -0.9166666667 + -0.7083333333n

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