Question

Solve (2x + 1) (2x + 6) - 7(x - 2) = 4(x + 1)(x - 1)-9x​

Answer 1

To solve the given equation, let's simplify and expand both sides:

`\displaystyle\sf (2x+1)(2x+6)-7(x-2)=4(x+1)(x-1)-9x`

Expanding the brackets:

`\displaystyle\sf (4x^(2)+13x+6)-7x+14=4(x^(2)-1)-9x`

Simplifying further:

`\displaystyle\sf 4x^(2)+13x+6-7x+14=4x^(2)-4-9x`

Combining like terms:

`\displaystyle\sf 4x^(2)+6x+20=4x^(2)-9x-4`

Subtracting
`\displaystyle\sf 4x^(2)` from both sides:

`\displaystyle\sf 6x+20=-9x-4`

Bringing all the variables to one side and the constants to the other side:

`\displaystyle\sf 6x+9x=-4-20`

`\displaystyle\sf 15x=-24`

Dividing both sides by
`\displaystyle\sf 15` to solve for
`\displaystyle\sf x`:

`\displaystyle\sf x=-(24)/(15)`

Simplifying the fraction:

`\displaystyle\sf x=-(8)/(5)`

Therefore, the solution to the equation is
`\displaystyle\sf x=-(8)/(5)`.

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Answer 2

x is equal to -34/16

Explanation:

Hey there!

In order to solve for x, we need to first simplify everything

After simplifying, it will look like this:

`(4x^2+14x+16)-7x+14=4x^2-4-9x`

Now you can simplify by combining like terms

`4x^2+7x+30=4x^2-9x-4`

You can cross out
`4x^2` from both sides and then simplify even more by again combining like terms

`16x+34=0\\16x=-34\\x=-34/16`

So x is equal to -34/16