y= -10 or 4
Explanationgiven
[tex]y^2+6y=40[/tex]
Step 1
factor
a)subtrac 40 in both sides
[tex]\begin{gathered} y^2+6y=40 \\ y^2+6y-40=40-40 \\ y^2+6y-40=0 \end{gathered}[/tex]
b)write 6y as 10y -4y
so
[tex]\begin{gathered} y^{2}+6y-40=0 \\ y^2+10y-4y-40=0 \end{gathered}[/tex]
c) group and facrtor the common term
[tex]\begin{gathered} y^{2}+10y-4y-40=0 \\ y(y+10)-4(y+10)=0 \\ (y+10)\text{ is the common factor, so} \\ (y+10)(y-4)=0 \end{gathered}[/tex]
so, the new expression is
[tex](y+10)(y-4)=0[/tex]
Step 2
solve for x
[tex](y+10)(y-4)=0[/tex]
when the product of 2 factors equals zero, it means one or both factors equals zero, so
[tex]\begin{gathered} (y+10)(y-4)=0 \\ (y+10)=0 \\ solve\text{ for y, subtract 10 in both sides} \\ (y+10)-10=0-10 \\ y=-10\Rightarrow solution \\ \end{gathered}[/tex]
and
[tex]\begin{gathered} (y+10)(y-4)=0 \\ (y-4)=0 \\ solve\text{ for y, add 4 in both sides} \\ (y-4)+4=0+4 \\ y=4\Rightarrow solution \\ \end{gathered}[/tex]
so, the answer is
y= -10 or 4
I hope this helps you
