# Solve for y y^3+3y^2=49y+147 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 the left side of the equation.
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 and solve.
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 and solve.
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 and solve.
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

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