7y2=280-21y

Add 21y to both sides of the equation.

7y2+21y=280

Move 280 to the left side of the equation by subtracting it from both sides.

7y2+21y-280=0

Factor 7 out of 7y2+21y-280.

Factor 7 out of 7y2.

7(y2)+21y-280=0

Factor 7 out of 21y.

7(y2)+7(3y)-280=0

Factor 7 out of -280.

7y2+7(3y)+7⋅-40=0

Factor 7 out of 7y2+7(3y).

7(y2+3y)+7⋅-40=0

Factor 7 out of 7(y2+3y)+7⋅-40.

7(y2+3y-40)=0

7(y2+3y-40)=0

Factor.

Factor y2+3y-40 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -40 and whose sum is 3.

-5,8

Write the factored form using these integers.

7((y-5)(y+8))=0

7((y-5)(y+8))=0

Remove unnecessary parentheses.

7(y-5)(y+8)=0

7(y-5)(y+8)=0

7(y-5)(y+8)=0

Divide each term in 7(y-5)(y+8)=0 by 7.

7(y-5)(y+8)7=07

Simplify 7(y-5)(y+8)7.

Cancel the common factor of 7.

Cancel the common factor.

7(y-5)(y+8)7=07

Divide (y-5)(y+8) by 1.

(y-5)(y+8)=07

(y-5)(y+8)=07

Expand (y-5)(y+8) using the FOIL Method.

Apply the distributive property.

y(y+8)-5(y+8)=07

Apply the distributive property.

y⋅y+y⋅8-5(y+8)=07

Apply the distributive property.

y⋅y+y⋅8-5y-5⋅8=07

y⋅y+y⋅8-5y-5⋅8=07

Simplify and combine like terms.

Simplify each term.

Multiply y by y.

y2+y⋅8-5y-5⋅8=07

Move 8 to the left of y.

y2+8⋅y-5y-5⋅8=07

Multiply -5 by 8.

y2+8y-5y-40=07

y2+8y-5y-40=07

Subtract 5y from 8y.

y2+3y-40=07

y2+3y-40=07

y2+3y-40=07

Divide 0 by 7.

y2+3y-40=0

y2+3y-40=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -40 and whose sum is 3.

-5,8

Write the factored form using these integers.

(y-5)(y+8)=0

(y-5)(y+8)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

y-5=0

y+8=0

Set the first factor equal to 0.

y-5=0

Add 5 to both sides of the equation.

y=5

y=5

Set the next factor equal to 0.

y+8=0

Subtract 8 from both sides of the equation.

y=-8

y=-8

The final solution is all the values that make (y-5)(y+8)=0 true.

y=5,-8

Solve for y 7y^2=280-21y