Find all real solutions of the equation by factoring. 6x(x-1)=21-x

amolent3u 2021-12-15 Answered
Find all real solutions of the equation by factoring.
6x(x-1)=21-x
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Expert Answer

Kirsten Davis
Answered 2021-12-16 Author has 27 answers
Step 1
We have to find all real solutions of the equation by factorizing:
6x(x-1)=21-x
Solving given equation,
6x(x-1)=21-x
6x26x=21x
6x26x+x=21
6x25x21=0
Now solving by factorization,
6x214x+9x21=0
2x(3x-7)+3(3x-7)=0
(3x-7)(2x+3)=0
Step 2
Either,
3x-7=0
3x=7
x=73
or,
2x+3=0
2x=-3
x=32
Hence, solutions of the equation are x=32,73.

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Hector Roberts
Answered 2021-12-17 Author has 31 answers
The given quadratic equation is 6x(x-1)=21-x
6x(x-1)=21-x [given equation]
6x26x=21x
6x26x+x=21x+x
6x25x=21
6x25x21=2121
6x25x21=0 [quadratic form]
6x2+9x14x21=0
3x(2x+3)-7(2x+3)=0
(3x-7)(2x+3)=0 [factor]
3x-7=0 or 3x+3=0 [zero-product property]
x=73 or x=32
The solutions are x=73 and x=32

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