Solve for c 3/2*(c-1)=1/2*(4c)+1

Math
32⋅(c-1)=12⋅(4c)+1
Simplify 32⋅(c-1).
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Apply the distributive property.
32c+32⋅-1=12⋅(4c)+1
Combine 32 and c.
3c2+32⋅-1=12⋅(4c)+1
Multiply 32⋅-1.
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Combine 32 and -1.
3c2+3⋅-12=12⋅(4c)+1
Multiply 3 by -1.
3c2+-32=12⋅(4c)+1
3c2+-32=12⋅(4c)+1
Move the negative in front of the fraction.
3c2-32=12⋅(4c)+1
3c2-32=12⋅(4c)+1
Cancel the common factor of 2.
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Factor 2 out of 4c.
3c2-32=12⋅(2(2c))+1
Cancel the common factor.
3c2-32=12⋅(2(2c))+1
Rewrite the expression.
3c2-32=2c+1
3c2-32=2c+1
Move all terms containing c to the left side of the equation.
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Subtract 2c from both sides of the equation.
3c2-32-2c=1
To write -2c as a fraction with a common denominator, multiply by 22.
3c2-2c⋅22-32=1
Combine -2c and 22.
3c2+-2c⋅22-32=1
Combine the numerators over the common denominator.
3c-2c⋅22-32=1
Combine the numerators over the common denominator.
3c-2c⋅2-32=1
Simplify the numerator.
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Multiply 2 by -2.
3c-4c-32=1
Subtract 4c from 3c.
-c-32=1
-c-32=1
Factor -1 out of -c.
-(c)-32=1
Rewrite -3 as -1(3).
-(c)-1(3)2=1
Factor -1 out of -(c)-1(3).
-(c+3)2=1
Rewrite -(c+3) as -1(c+3).
-1(c+3)2=1
Move the negative in front of the fraction.
-c+32=1
-c+32=1
Multiply both sides of the equation by -2.
-2⋅(-c+32)=-2⋅1
Simplify both sides of the equation.
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Simplify -2⋅(-c+32).
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Cancel the common factor of 2.
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Move the leading negative in -c+32 into the numerator.
-2⋅-(c+3)2=-2⋅1
Factor 2 out of -2.
2(-1)⋅-(c+3)2=-2⋅1
Cancel the common factor.
2⋅-1⋅-(c+3)2=-2⋅1
Rewrite the expression.
-1⋅(-(c+3))=-2⋅1
-1⋅(-(c+3))=-2⋅1
Multiply.
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Multiply -1 by -1.
1⋅(c+3)=-2⋅1
Multiply c+3 by 1.
c+3=-2⋅1
c+3=-2⋅1
c+3=-2⋅1
Multiply -2 by 1.
c+3=-2
c+3=-2
Move all terms not containing c to the right side of the equation.
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Subtract 3 from both sides of the equation.
c=-2-3
Subtract 3 from -2.
c=-5
c=-5
Solve for c 3/2*(c-1)=1/2*(4c)+1

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