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

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

Simplifying
(3a + 4b + 2c) + -1(-3a + 4b + -2c) + -1(5a + -3b) = 0

Remove parenthesis around (3a + 4b + 2c)
3a + 4b + 2c + -1(-3a + 4b + -2c) + -1(5a + -3b) = 0
3a + 4b + 2c + (-3a * -1 + 4b * -1 + -2c * -1) + -1(5a + -3b) = 0
3a + 4b + 2c + (3a + -4b + 2c) + -1(5a + -3b) = 0
3a + 4b + 2c + 3a + -4b + 2c + (5a * -1 + -3b * -1) = 0
3a + 4b + 2c + 3a + -4b + 2c + (-5a + 3b) = 0

Reorder the terms:
3a + 3a + -5a + 4b + -4b + 3b + 2c + 2c = 0

Combine like terms: 3a + 3a = 6a
6a + -5a + 4b + -4b + 3b + 2c + 2c = 0

Combine like terms: 6a + -5a = 1a
1a + 4b + -4b + 3b + 2c + 2c = 0

Combine like terms: 4b + -4b = 0
1a + 0 + 3b + 2c + 2c = 0
1a + 3b + 2c + 2c = 0

Combine like terms: 2c + 2c = 4c
1a + 3b + 4c = 0

Solving
1a + 3b + 4c = 0

Solving for variable 'a'.

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

Add '-3b' to each side of the equation.
1a + 3b + -3b + 4c = 0 + -3b

Combine like terms: 3b + -3b = 0
1a + 0 + 4c = 0 + -3b
1a + 4c = 0 + -3b
Remove the zero:
1a + 4c = -3b

Add '-4c' to each side of the equation.
1a + 4c + -4c = -3b + -4c

Combine like terms: 4c + -4c = 0
1a + 0 = -3b + -4c
1a = -3b + -4c

Divide each side by '1'.
a = -3b + -4c

Simplifying
a = -3b + -4c