# Solve for y 5/3y+1/3y=5y+70/3+5/3y

53y+13y=5y+703+53y
Simplify 53y+13y.
Simplify each term.
Combine 53 and y.
5y3+13y=5y+703+53y
Combine 13 and y.
5y3+y3=5y+703+53y
5y3+y3=5y+703+53y
Simplify terms.
Combine the numerators over the common denominator.
5y+y3=5y+703+53y
6y3=5y+703+53y
Cancel the common factor of 6 and 3.
Factor 3 out of 6y.
3(2y)3=5y+703+53y
Cancel the common factors.
Factor 3 out of 3.
3(2y)3(1)=5y+703+53y
Cancel the common factor.
3(2y)3⋅1=5y+703+53y
Rewrite the expression.
2y1=5y+703+53y
Divide 2y by 1.
2y=5y+703+53y
2y=5y+703+53y
2y=5y+703+53y
2y=5y+703+53y
2y=5y+703+53y
Simplify 5y+703+53y.
Combine 53 and y.
2y=5y+703+5y3
To write 5y as a fraction with a common denominator, multiply by 33.
2y=5y⋅33+5y3+703
Simplify terms.
Combine 5y and 33.
2y=5y⋅33+5y3+703
Combine the numerators over the common denominator.
2y=5y⋅3+5y3+703
Combine the numerators over the common denominator.
2y=5y⋅3+5y+703
2y=5y⋅3+5y+703
Simplify the numerator.
Factor 5 out of 5y⋅3+5y+70.
Factor 5 out of 5y⋅3.
2y=5(y⋅3)+5y+703
Factor 5 out of 5y.
2y=5(y⋅3)+5(y)+703
Factor 5 out of 70.
2y=5(y⋅3)+5y+5⋅143
Factor 5 out of 5(y⋅3)+5y.
2y=5(y⋅3+y)+5⋅143
Factor 5 out of 5(y⋅3+y)+5⋅14.
2y=5(y⋅3+y+14)3
2y=5(y⋅3+y+14)3
Reorder y and 3.
2y=5(3⋅y+y+14)3
2y=5(4⋅y+14)3
2y=5(4⋅y+14)3
Factor 2 out of 4⋅y+14.
Factor 2 out of 4⋅y.
2y=5(2(2⋅y)+14)3
Factor 2 out of 14.
2y=5(2(2⋅y)+2(7))3
Factor 2 out of 2(2⋅y)+2(7).
2y=5(2(2⋅y+7))3
2y=5(2(2⋅y+7))3
Remove unnecessary parentheses.
2y=5⋅2(2y+7)3
Multiply 5 by 2.
2y=10(2y+7)3
2y=10(2y+7)3
2y=10(2y+7)3
Move all terms containing y to the left side of the equation.
Subtract 10(2y+7)3 from both sides of the equation.
2y-10(2y+7)3=0
To write 2y as a fraction with a common denominator, multiply by 33.
2y⋅33-10(2y+7)3=0
Combine 2y and 33.
2y⋅33-10(2y+7)3=0
Combine the numerators over the common denominator.
2y⋅3-10(2y+7)3=0
Simplify the numerator.
Factor 2 out of 2y⋅3-10(2y+7).
Factor 2 out of 2y⋅3.
2(y⋅3)-10(2y+7)3=0
Factor 2 out of -10(2y+7).
2(y⋅3)+2(-5(2y+7))3=0
Factor 2 out of 2(y⋅3)+2(-5(2y+7)).
2(y⋅3-5(2y+7))3=0
2(y⋅3-5(2y+7))3=0
Move 3 to the left of y.
2(3⋅y-5(2y+7))3=0
Apply the distributive property.
2(3y-5(2y)-5⋅7)3=0
Multiply 2 by -5.
2(3y-10y-5⋅7)3=0
Multiply -5 by 7.
2(3y-10y-35)3=0
Subtract 10y from 3y.
2(-7y-35)3=0
Factor 7 out of -7y-35.
Factor 7 out of -7y.
2(7(-y)-35)3=0
Factor 7 out of -35.
2(7(-y)+7(-5))3=0
Factor 7 out of 7(-y)+7(-5).
2(7(-y-5))3=0
2⋅7(-y-5)3=0
Multiply 2 by 7.
14(-y-5)3=0
14(-y-5)3=0
Factor -1 out of -y.
14(-(y)-5)3=0
Rewrite -5 as -1(5).
14(-(y)-1(5))3=0
Factor -1 out of -(y)-1(5).
14(-(y+5))3=0
Rewrite -(y+5) as -1(y+5).
14(-1(y+5))3=0
Move the negative in front of the fraction.
-14(y+5)3=0
-14(y+5)3=0
Multiply both sides of the equation by -314.
-314⋅(-14(y+5)3)=-314⋅0
Simplify both sides of the equation.
Simplify -314⋅(-14(y+5)3).
Cancel the common factor of 3.
Move the leading negative in -314 into the numerator.
-314⋅(-14(y+5)3)=-314⋅0
Move the leading negative in -14(y+5)3 into the numerator.
-314⋅-14(y+5)3=-314⋅0
Factor 3 out of -3.
3(-1)14⋅-14(y+5)3=-314⋅0
Cancel the common factor.
3⋅-114⋅-14(y+5)3=-314⋅0
Rewrite the expression.
-114⋅(-14(y+5))=-314⋅0
-114⋅(-14(y+5))=-314⋅0
Cancel the common factor of 14.
Factor 14 out of -14(y+5).
-114⋅(14(-(y+5)))=-314⋅0
Cancel the common factor.
-114⋅(14(-(y+5)))=-314⋅0
Rewrite the expression.
-1⋅(-(y+5))=-314⋅0
-1⋅(-(y+5))=-314⋅0
Multiply.
Multiply -1 by -1.
1⋅(y+5)=-314⋅0
Multiply y+5 by 1.
y+5=-314⋅0
y+5=-314⋅0
y+5=-314⋅0
Multiply -314⋅0.
Multiply 0 by -1.
y+5=0(314)
Multiply 0 by 314.
y+5=0
y+5=0
y+5=0
Subtract 5 from both sides of the equation.
y=-5
Solve for y 5/3y+1/3y=5y+70/3+5/3y

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