3a+b-45=2a+4b-465.23+-a+507.23b

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Solution for 3a+b-45=2a+4b-465.23+-a+507.23b equation: 


Simplifying
3a + b + -45 = 2a + 4b + -465.23 + -1a + 507.23b

Reorder the terms:
-45 + 3a + b = 2a + 4b + -465.23 + -1a + 507.23b

Reorder the terms:
-45 + 3a + b = -465.23 + 2a + -1a + 4b + 507.23b

Combine like terms: 2a + -1a = 1a
-45 + 3a + b = -465.23 + 1a + 4b + 507.23b

Combine like terms: 4b + 507.23b = 511.23b
-45 + 3a + b = -465.23 + 1a + 511.23b

Solving
-45 + 3a + b = -465.23 + 1a + 511.23b

Solving for variable 'a'.

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

Add '-1a' to each side of the equation.
-45 + 3a + -1a + b = -465.23 + 1a + -1a + 511.23b

Combine like terms: 3a + -1a = 2a
-45 + 2a + b = -465.23 + 1a + -1a + 511.23b

Combine like terms: 1a + -1a = 0
-45 + 2a + b = -465.23 + 0 + 511.23b
-45 + 2a + b = -465.23 + 511.23b

Add '45' to each side of the equation.
-45 + 2a + 45 + b = -465.23 + 45 + 511.23b

Reorder the terms:
-45 + 45 + 2a + b = -465.23 + 45 + 511.23b

Combine like terms: -45 + 45 = 0
0 + 2a + b = -465.23 + 45 + 511.23b
2a + b = -465.23 + 45 + 511.23b

Combine like terms: -465.23 + 45 = -420.23
2a + b = -420.23 + 511.23b

Add '-1b' to each side of the equation.
2a + b + -1b = -420.23 + 511.23b + -1b

Combine like terms: b + -1b = 0
2a + 0 = -420.23 + 511.23b + -1b
2a = -420.23 + 511.23b + -1b

Combine like terms: 511.23b + -1b = 510.23b
2a = -420.23 + 510.23b

Divide each side by '2'.
a = -210.115 + 255.115b

Simplifying
a = -210.115 + 255.115b

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