6(a-3b+5c)-4(5b-c+2a)-5(2a-4c+3b)=

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Solution for 6(a-3b+5c)-4(5b-c+2a)-5(2a-4c+3b)= equation: 


Simplifying
6(a + -3b + 5c) + -4(5b + -1c + 2a) + -5(2a + -4c + 3b) = 0
(a * 6 + -3b * 6 + 5c * 6) + -4(5b + -1c + 2a) + -5(2a + -4c + 3b) = 0
(6a + -18b + 30c) + -4(5b + -1c + 2a) + -5(2a + -4c + 3b) = 0

Reorder the terms:
6a + -18b + 30c + -4(2a + 5b + -1c) + -5(2a + -4c + 3b) = 0
6a + -18b + 30c + (2a * -4 + 5b * -4 + -1c * -4) + -5(2a + -4c + 3b) = 0
6a + -18b + 30c + (-8a + -20b + 4c) + -5(2a + -4c + 3b) = 0

Reorder the terms:
6a + -18b + 30c + -8a + -20b + 4c + -5(2a + 3b + -4c) = 0
6a + -18b + 30c + -8a + -20b + 4c + (2a * -5 + 3b * -5 + -4c * -5) = 0
6a + -18b + 30c + -8a + -20b + 4c + (-10a + -15b + 20c) = 0

Reorder the terms:
6a + -8a + -10a + -18b + -20b + -15b + 30c + 4c + 20c = 0

Combine like terms: 6a + -8a = -2a
-2a + -10a + -18b + -20b + -15b + 30c + 4c + 20c = 0

Combine like terms: -2a + -10a = -12a
-12a + -18b + -20b + -15b + 30c + 4c + 20c = 0

Combine like terms: -18b + -20b = -38b
-12a + -38b + -15b + 30c + 4c + 20c = 0

Combine like terms: -38b + -15b = -53b
-12a + -53b + 30c + 4c + 20c = 0

Combine like terms: 30c + 4c = 34c
-12a + -53b + 34c + 20c = 0

Combine like terms: 34c + 20c = 54c
-12a + -53b + 54c = 0

Solving
-12a + -53b + 54c = 0

Solving for variable 'a'.

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

Add '53b' to each side of the equation.
-12a + -53b + 53b + 54c = 0 + 53b

Combine like terms: -53b + 53b = 0
-12a + 0 + 54c = 0 + 53b
-12a + 54c = 0 + 53b
Remove the zero:
-12a + 54c = 53b

Add '-54c' to each side of the equation.
-12a + 54c + -54c = 53b + -54c

Combine like terms: 54c + -54c = 0
-12a + 0 = 53b + -54c
-12a = 53b + -54c

Divide each side by '-12'.
a = -4.416666667b + 4.5c

Simplifying
a = -4.416666667b + 4.5c

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