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

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


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

Combine like terms: -2b + 3b = 1b
2a + 1b + 3c = 4(b + -1c)
2a + 1b + 3c = (b * 4 + -1c * 4)
2a + 1b + 3c = (4b + -4c)

Solving
2a + 1b + 3c = 4b + -4c

Solving for variable 'a'.

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

Add '-1b' to each side of the equation.
2a + 1b + -1b + 3c = 4b + -1b + -4c

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

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

Add '-3c' to each side of the equation.
2a + 3c + -3c = 3b + -4c + -3c

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

Combine like terms: -4c + -3c = -7c
2a = 3b + -7c

Divide each side by '2'.
a = 1.5b + -3.5c

Simplifying
a = 1.5b + -3.5c

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