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Question

Solve the following equation:
x24x+32=16x

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Solution

x24x+32=16x
x(x4)=16x32
x(x2)(x+2)=16(x2)
Let x2=t
(t+2)2(t)(t+4)=16t
t=0 is a solution
(t2+4t+4)(t+4)=16
t3+8t2+20t+16=16
t(t2+8t+20)=0
t=0 is only solution
x2=0
x=2
x=4

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