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

Math
6c7=2(c+5)3-4
Multiply both sides of the equation by 7.
6c=(2(c+5)3-4)⋅(7)
Simplify (2(c+5)3-4)⋅(7).
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To write -4 as a fraction with a common denominator, multiply by 33.
6c=(2(c+5)3-4⋅33)⋅7
Simplify terms.
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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.
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Factor 2 out of 2(c+5)-4⋅3.
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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.
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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
Move all terms containing c to the left side of the equation.
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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.
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Factor 2 out of 6c⋅3-14(c-1).
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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)
Simplify 2(2c+7).
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Apply the distributive property.
2(2c)+2⋅7=0⋅(3)
Multiply.
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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 by 4 and simplify.
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Divide each term in 4c=-14 by 4.
4c4=-144
Cancel the common factor of 4.
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Cancel the common factor.
4c4=-144
Divide c by 1.
c=-144
c=-144
Simplify -144.
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Cancel the common factor of -14 and 4.
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Factor 2 out of -14.
c=2(-7)4
Cancel the common factors.
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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

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