6c7=2(c+5)3-4

Multiply both sides of the equation by 7.

6c=(2(c+5)3-4)⋅(7)

To write -4 as a fraction with a common denominator, multiply by 33.

6c=(2(c+5)3-4⋅33)⋅7

Simplify terms.

Combine -4 and 33.

6c=(2(c+5)3+-4⋅33)⋅7

Combine the numerators over the common denominator.

6c=2(c+5)-4⋅33⋅7

6c=2(c+5)-4⋅33⋅7

Simplify the numerator.

Factor 2 out of 2(c+5)-4⋅3.

Factor 2 out of -4⋅3.

6c=2(c+5)+2(-2⋅3)3⋅7

Factor 2 out of 2(c+5)+2(-2⋅3).

6c=2(c+5-2⋅3)3⋅7

6c=2(c+5-2⋅3)3⋅7

Multiply -2 by 3.

6c=2(c+5-6)3⋅7

Subtract 6 from 5.

6c=2(c-1)3⋅7

6c=2(c-1)3⋅7

Multiply 2(c-1)3⋅7.

Combine 2(c-1)3 and 7.

6c=2(c-1)⋅73

Multiply 7 by 2.

6c=14(c-1)3

6c=14(c-1)3

6c=14(c-1)3

Subtract 14(c-1)3 from both sides of the equation.

6c-14(c-1)3=0

To write 6c as a fraction with a common denominator, multiply by 33.

6c⋅33-14(c-1)3=0

Combine 6c and 33.

6c⋅33-14(c-1)3=0

Combine the numerators over the common denominator.

6c⋅3-14(c-1)3=0

Simplify the numerator.

Factor 2 out of 6c⋅3-14(c-1).

Factor 2 out of 6c⋅3.

2(3c⋅3)-14(c-1)3=0

Factor 2 out of -14(c-1).

2(3c⋅3)+2(-7(c-1))3=0

Factor 2 out of 2(3c⋅3)+2(-7(c-1)).

2(3c⋅3-7(c-1))3=0

2(3c⋅3-7(c-1))3=0

Multiply 3 by 3.

2(9c-7(c-1))3=0

Apply the distributive property.

2(9c-7c-7⋅-1)3=0

Multiply -7 by -1.

2(9c-7c+7)3=0

Subtract 7c from 9c.

2(2c+7)3=0

2(2c+7)3=0

2(2c+7)3=0

Multiply both sides of the equation by 3.

2(2c+7)=0⋅(3)

Apply the distributive property.

2(2c)+2⋅7=0⋅(3)

Multiply.

Multiply 2 by 2.

4c+2⋅7=0⋅(3)

Multiply 2 by 7.

4c+14=0⋅(3)

4c+14=0⋅(3)

4c+14=0⋅(3)

Multiply 0 by 3.

4c+14=0

Subtract 14 from both sides of the equation.

4c=-14

Divide each term in 4c=-14 by 4.

4c4=-144

Cancel the common factor of 4.

Cancel the common factor.

4c4=-144

Divide c by 1.

c=-144

c=-144

Simplify -144.

Cancel the common factor of -14 and 4.

Factor 2 out of -14.

c=2(-7)4

Cancel the common factors.

Factor 2 out of 4.

c=2⋅-72⋅2

Cancel the common factor.

c=2⋅-72⋅2

Rewrite the expression.

c=-72

c=-72

c=-72

Move the negative in front of the fraction.

c=-72

c=-72

c=-72

The result can be shown in multiple forms.

Exact Form:

c=-72

Decimal Form:

c=-3.5

Mixed Number Form:

c=-312

Solve for c (6c)/7=(2(c+5))/3-4