Solve Equation By Factoring

Factor.

y^6 - 9y^4 - 4y^2 = -36

y^6 - 9y^4 - 4y^2 +36 = 0

Now factor it by grouping the polynomial:
(y^6 - 9y^4) + (- 4y^2 +36) = 0
y^4(y^2 -9) -4(y^2 -9) = 0

The y^4 and -4 goes together like so
(y^4 -4)(y^2 -9) = 0

Factor again
(y^2-2)(y^2+2)(y+3)(y-3) = 0

Set each to zero and solve
y^2-2=0
y=±√ 2

y^2+2=0
y=√ -2
y= ± i √2

y-3=0
y=3

y+3=0
y=-3
--------------------------------------…
y = ±√ 2, ± i √2, -3, 3

y^6 - 9y^4 - 4y^2 + 36 = 0
y^4 * (y^2 - 9) - 4 * (y^2 - 9) = 0
(y^4 - 4) * (y^2 - 9) = 0
(y^2 - 2) * (y^2 + 2) * (y - 3) * (y + 3) = 0


y^2 - 2 = 0
y^2 = 2
y = -sqrt(2) , sqrt(2)

y^2 + 2 = 0
y^2 = -2
y = -i * sqrt(2) , i * sqrt(2)

y - 3 = 0
y = 3

y + 3 = 0
y = -3


y = -sqrt(2) , sqrt(2) , -3 , 3 , -i * sqrt(2) , i * sqrt(2)