45y+14⋅(y-5)=y+15

Move y+15 to the left side of the equation by subtracting it from both sides.

45y+14⋅(y-5)-y+15=0

Find the common denominator.

Write 45y as a fraction with denominator 1.

45y1+14⋅(y-5)-y+15=0

Multiply 45y1 by 55.

45y1⋅55+14⋅(y-5)-y+15=0

Multiply 45y1 and 55.

45y⋅55+14⋅(y-5)-y+15=0

Write 14⋅(y-5) as a fraction with denominator 1.

45y⋅55+14⋅(y-5)1-y+15=0

Multiply 14⋅(y-5)1 by 55.

45y⋅55+14⋅(y-5)1⋅55-y+15=0

Multiply 14⋅(y-5)1 and 55.

45y⋅55+14⋅(y-5)⋅55-y+15=0

45y⋅55+14⋅(y-5)⋅55-y+15=0

Combine the numerators over the common denominator.

45y⋅5+14⋅(y-5)⋅5-(y+1)5=0

Simplify the numerator.

Combine 45 and y.

4y5⋅5+14⋅(y-5)⋅5-(y+1)5=0

Cancel the common factor of 5.

Cancel the common factor.

4y5⋅5+14⋅(y-5)⋅5-(y+1)5=0

Rewrite the expression.

4y+14⋅(y-5)⋅5-(y+1)5=0

4y+14⋅(y-5)⋅5-(y+1)5=0

Apply the distributive property.

4y+(14y+14⋅-5)⋅5-(y+1)5=0

Combine 14 and y.

4y+(y4+14⋅-5)⋅5-(y+1)5=0

Combine 14 and -5.

4y+(y4+-54)⋅5-(y+1)5=0

Move the negative in front of the fraction.

4y+(y4-54)⋅5-(y+1)5=0

Apply the distributive property.

4y+y4⋅5-54⋅5-(y+1)5=0

Combine y4 and 5.

4y+y⋅54-54⋅5-(y+1)5=0

Multiply -54⋅5.

Multiply 5 by -1.

4y+y⋅54-5(54)-(y+1)5=0

Combine -5 and 54.

4y+y⋅54+-5⋅54-(y+1)5=0

Multiply -5 by 5.

4y+y⋅54+-254-(y+1)5=0

4y+y⋅54+-254-(y+1)5=0

Simplify each term.

Move 5 to the left of y.

4y+5⋅y4+-254-(y+1)5=0

Move the negative in front of the fraction.

4y+5y4-254-(y+1)5=0

4y+5y4-254-(y+1)5=0

Apply the distributive property.

4y+5y4-254-y-1⋅15=0

Multiply -1 by 1.

4y+5y4-254-y-15=0

To write 4y as a fraction with a common denominator, multiply by 44.

4y⋅44+5y4-254-y-15=0

Combine 4y and 44.

4y⋅44+5y4-254-y-15=0

Combine the numerators over the common denominator.

4y⋅4+5y4-254-y-15=0

Combine the numerators over the common denominator.

4y⋅4+5y-254-y-15=0

To write -y as a fraction with a common denominator, multiply by 44.

4y⋅4+5y-254-y⋅44-15=0

Combine -y and 44.

4y⋅4+5y-254+-y⋅44-15=0

Combine the numerators over the common denominator.

4y⋅4+5y-25-y⋅44-15=0

To write -1 as a fraction with a common denominator, multiply by 44.

4y⋅4+5y-25-y⋅44-1⋅445=0

Combine -1 and 44.

4y⋅4+5y-25-y⋅44+-1⋅445=0

Combine the numerators over the common denominator.

4y⋅4+5y-25-y⋅4-1⋅445=0

Reorder terms.

4⋅4y-1⋅4y+5y-25-1⋅445=0

Rewrite 4⋅4y-1⋅4y+5y-25-1⋅44 in a factored form.

Multiply 4 by 4.

16y-1⋅4y+5y-25-1⋅445=0

Multiply -1 by 4.

16y-4y+5y-25-1⋅445=0

Multiply -1 by 4.

16y-4y+5y-25-445=0

Subtract 4y from 16y.

12y+5y-25-445=0

Add 12y and 5y.

17y-25-445=0

Subtract 4 from -25.

17y-2945=0

17y-2945=0

17y-2945=0

Multiply the numerator by the reciprocal of the denominator.

17y-294⋅15=0

Multiply 17y-294⋅15.

Multiply 17y-294 and 15.

17y-294⋅5=0

Multiply 4 by 5.

17y-2920=0

17y-2920=0

17y-2920=0

Since this is the only denominator in the list, the result is the LCD: 20.

20

Multiply each term in 17y-2920=0 by 20.

17y-2920⋅20=0⋅20

Cancel the common factor of 20.

Cancel the common factor.

17y-2920⋅20=0⋅20

Rewrite the expression.

17y-29=0⋅20

17y-29=0⋅20

Multiply 0 by 20.

17y-29=0

17y-29=0

Add 29 to both sides of the equation.

17y=29

Divide each term in 17y=29 by 17.

17y17=2917

Cancel the common factor of 17.

Cancel the common factor.

17y17=2917

Divide y by 1.

y=2917

y=2917

y=2917

The result can be shown in multiple forms.

Exact Form:

y=2917

Decimal Form:

y=1.70588235…

Mixed Number Form:

y=11217

Solve for y 4/5y+1/4*(y-5)=(y+1)/5