32⋅(c-1)=12⋅(4c)+1

Apply the distributive property.

32c+32⋅-1=12⋅(4c)+1

Combine 32 and c.

3c2+32⋅-1=12⋅(4c)+1

Multiply 32⋅-1.

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

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

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.

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 -2⋅(-c+32).

Cancel the common factor of 2.

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.

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

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