52y-13=-12

Combine 52 and y.

5y2-13=-12

Add 13 to both sides of the equation.

5y2=-12+13

To write -12 as a fraction with a common denominator, multiply by 33.

5y2=-12⋅33+13

To write 13 as a fraction with a common denominator, multiply by 22.

5y2=-12⋅33+13⋅22

Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.

Multiply 12 and 33.

5y2=-32⋅3+13⋅22

Multiply 2 by 3.

5y2=-36+13⋅22

Multiply 13 and 22.

5y2=-36+23⋅2

Multiply 3 by 2.

5y2=-36+26

5y2=-36+26

Combine the numerators over the common denominator.

5y2=-3+26

Add -3 and 2.

5y2=-16

Move the negative in front of the fraction.

5y2=-16

5y2=-16

Multiply both sides of the equation by 25.

25⋅5y2=25⋅(-16)

Simplify 25⋅5y2.

Cancel the common factor of 2.

Cancel the common factor.

25⋅5y2=25⋅(-16)

Rewrite the expression.

15⋅(5y)=25⋅(-16)

15⋅(5y)=25⋅(-16)

Cancel the common factor of 5.

Factor 5 out of 5y.

15⋅(5(y))=25⋅(-16)

Cancel the common factor.

15⋅(5y)=25⋅(-16)

Rewrite the expression.

y=25⋅(-16)

y=25⋅(-16)

y=25⋅(-16)

Simplify 25⋅(-16).

Cancel the common factor of 2.

Move the leading negative in -16 into the numerator.

y=25⋅-16

Factor 2 out of 6.

y=25⋅-12(3)

Cancel the common factor.

y=25⋅-12⋅3

Rewrite the expression.

y=15⋅-13

y=15⋅-13

Multiply 15 and -13.

y=-15⋅3

Simplify the expression.

Multiply 5 by 3.

y=-115

Move the negative in front of the fraction.

y=-115

y=-115

y=-115

y=-115

The result can be shown in multiple forms.

Exact Form:

y=-115

Decimal Form:

y=-0.06‾

Solve for y 5/2y-1/3=-1/2