y3+3y2=49y+147

Subtract 49y from both sides of the equation.

y3+3y2-49y=147

Move 147 to the left side of the equation by subtracting it from both sides.

y3+3y2-49y-147=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(y3+3y2)-49y-147=0

Factor out the greatest common factor (GCF) from each group.

y2(y+3)-49(y+3)=0

y2(y+3)-49(y+3)=0

Factor the polynomial by factoring out the greatest common factor, y+3.

(y+3)(y2-49)=0

Rewrite 49 as 72.

(y+3)(y2-72)=0

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=y and b=7.

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

Remove unnecessary parentheses.

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

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

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

y+7=0

y-7=0

Set the first factor equal to 0.

y+3=0

Subtract 3 from both sides of the equation.

y=-3

y=-3

Set the next factor equal to 0.

y+7=0

Subtract 7 from both sides of the equation.

y=-7

y=-7

Set the next factor equal to 0.

y-7=0

Add 7 to both sides of the equation.

y=7

y=7

The final solution is all the values that make (y+3)(y+7)(y-7)=0 true.

y=-3,-7,7

Solve for y y^3+3y^2=49y+147