# Solve for d 1/6d+2/3=1/4*(d-2)

16d+23=14⋅(d-2)
Combine 16 and d.
d6+23=14⋅(d-2)
Simplify 14⋅(d-2).
Apply the distributive property.
d6+23=14d+14⋅-2
Combine 14 and d.
d6+23=d4+14⋅-2
Cancel the common factor of 2.
Factor 2 out of 4.
d6+23=d4+12(2)⋅-2
Factor 2 out of -2.
d6+23=d4+12⋅2⋅(2⋅-1)
Cancel the common factor.
d6+23=d4+12⋅2⋅(2⋅-1)
Rewrite the expression.
d6+23=d4+12⋅-1
d6+23=d4+12⋅-1
Combine 12 and -1.
d6+23=d4+-12
Move the negative in front of the fraction.
d6+23=d4-12
d6+23=d4-12
Move all terms containing d to the left side of the equation.
Subtract d4 from both sides of the equation.
d6+23-d4=-12
To write d6 as a fraction with a common denominator, multiply by 22.
d6⋅22-d4+23=-12
To write -d4 as a fraction with a common denominator, multiply by 33.
d6⋅22-d4⋅33+23=-12
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
Multiply d6 and 22.
d⋅26⋅2-d4⋅33+23=-12
Multiply 6 by 2.
d⋅212-d4⋅33+23=-12
Multiply d4 and 33.
d⋅212-d⋅34⋅3+23=-12
Multiply 4 by 3.
d⋅212-d⋅312+23=-12
d⋅212-d⋅312+23=-12
Combine the numerators over the common denominator.
d⋅2-d⋅312+23=-12
Simplify each term.
Simplify the numerator.
Factor d out of d⋅2-d⋅3.
Factor d out of d⋅2.
d(2)-d⋅312+23=-12
Factor d out of -d⋅3.
d(2)+d(-1⋅3)12+23=-12
Factor d out of d(2)+d(-1⋅3).
d(2-1⋅3)12+23=-12
d(2-1⋅3)12+23=-12
Multiply -1 by 3.
d(2-3)12+23=-12
Subtract 3 from 2.
d⋅-112+23=-12
d⋅-112+23=-12
Move -1 to the left of d.
-1⋅d12+23=-12
Move the negative in front of the fraction.
-d12+23=-12
-d12+23=-12
-d12+23=-12
Move all terms not containing d to the right side of the equation.
Subtract 23 from both sides of the equation.
-d12=-12-23
To write -12 as a fraction with a common denominator, multiply by 33.
-d12=-12⋅33-23
To write -23 as a fraction with a common denominator, multiply by 22.
-d12=-12⋅33-23⋅22
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 12 and 33.
-d12=-32⋅3-23⋅22
Multiply 2 by 3.
-d12=-36-23⋅22
Multiply 23 and 22.
-d12=-36-2⋅23⋅2
Multiply 3 by 2.
-d12=-36-2⋅26
-d12=-36-2⋅26
Combine the numerators over the common denominator.
-d12=-3-2⋅26
Simplify the numerator.
Multiply -2 by 2.
-d12=-3-46
Subtract 4 from -3.
-d12=-76
-d12=-76
Move the negative in front of the fraction.
-d12=-76
-d12=-76
Multiply both sides of the equation by -12.
-12⋅(-d12)=-12⋅(-76)
Simplify both sides of the equation.
Simplify -12⋅(-d12).
Cancel the common factor of 12.
Move the leading negative in -d12 into the numerator.
-12⋅-d12=-12⋅(-76)
Factor 12 out of -12.
12(-1)⋅-d12=-12⋅(-76)
Cancel the common factor.
12⋅-1⋅-d12=-12⋅(-76)
Rewrite the expression.
-1⋅(-d)=-12⋅(-76)
-1⋅(-d)=-12⋅(-76)
Multiply.
Multiply -1 by -1.
1⋅d=-12⋅(-76)
Multiply d by 1.
d=-12⋅(-76)
d=-12⋅(-76)
d=-12⋅(-76)
Simplify -12⋅(-76).
Cancel the common factor of 6.
Move the leading negative in -76 into the numerator.
d=-12⋅-76
Factor 6 out of -12.
d=6(-2)⋅-76
Cancel the common factor.
d=6⋅-2⋅-76
Rewrite the expression.
d=-2⋅-7
d=-2⋅-7
Multiply -2 by -7.
d=14
d=14
d=14
Solve for d 1/6d+2/3=1/4*(d-2)

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