# Solve for a (a*2/3)+(b*5/6-30)+c=180 (a⋅23)+(b⋅56-30)+c=180
Simplify each term.
Combine a and 23.
a⋅23+b⋅56-30+c=180
Move 2 to the left of a.
2⋅a3+b⋅56-30+c=180
Combine b and 56.
2a3+b⋅56-30+c=180
Move 5 to the left of b.
2a3+5b6-30+c=180
2a3+5b6-30+c=180
Move all terms not containing a to the right side of the equation.
Subtract 5b6 from both sides of the equation.
2a3-30+c=180-5b6
Add 30 to both sides of the equation.
2a3+c=180-5b6+30
Subtract c from both sides of the equation.
2a3=180-5b6+30-c
Add 180 and 30.
2a3=-5b6+210-c
2a3=-5b6+210-c
Multiply both sides of the equation by 32.
32⋅2a3=32⋅(-5b6+210-c)
Simplify both sides of the equation.
Simplify 32⋅2a3.
Cancel the common factor of 3.
Cancel the common factor.
32⋅2a3=32⋅(-5b6+210-c)
Rewrite the expression.
12⋅(2a)=32⋅(-5b6+210-c)
12⋅(2a)=32⋅(-5b6+210-c)
Cancel the common factor of 2.
Factor 2 out of 2a.
12⋅(2(a))=32⋅(-5b6+210-c)
Cancel the common factor.
12⋅(2a)=32⋅(-5b6+210-c)
Rewrite the expression.
a=32⋅(-5b6+210-c)
a=32⋅(-5b6+210-c)
a=32⋅(-5b6+210-c)
Simplify 32⋅(-5b6+210-c).
Apply the distributive property.
a=32(-5b6)+32⋅210+32(-c)
Simplify.
Cancel the common factor of 3.
Move the leading negative in -5b6 into the numerator.
a=32⋅-5b6+32⋅210+32(-c)
Factor 3 out of 6.
a=32⋅-5b3(2)+32⋅210+32(-c)
Cancel the common factor.
a=32⋅-5b3⋅2+32⋅210+32(-c)
Rewrite the expression.
a=12⋅-5b2+32⋅210+32(-c)
a=12⋅-5b2+32⋅210+32(-c)
Multiply 12 and -5b2.
a=-5b2⋅2+32⋅210+32(-c)
Multiply 2 by 2.
a=-5b4+32⋅210+32(-c)
Cancel the common factor of 2.
Factor 2 out of 210.
a=-5b4+32⋅(2(105))+32(-c)
Cancel the common factor.
a=-5b4+32⋅(2⋅105)+32(-c)
Rewrite the expression.
a=-5b4+3⋅105+32(-c)
a=-5b4+3⋅105+32(-c)
Multiply 3 by 105.
a=-5b4+315+32(-c)
Combine 32 and c.
a=-5b4+315-3c2
a=-5b4+315-3c2
Move the negative in front of the fraction.
a=-5b4+315-3c2
a=-5b4+315-3c2
a=-5b4+315-3c2
Move 315.
a=-5b4-3c2+315
Solve for a (a*2/3)+(b*5/6-30)+c=180

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