Solve the following inequalities: x^2+5x+12 > 6

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`(x^2+5x+12)gt6`

Rearranging,

`x^2+5x+6gt0`

Changing into factors,

`(x+2)(x+3)gt0`

**For this to be positive, both of the factors are negative or both of the factors are positive.**

Therefore, one solution is,

`x+2lt0 and x+3lt0`

`xlt-2` and `xlt-3`

The common solution for this is `x lt-3` .

The other solution,

`x+2gt0` and `x+3gt0`

`xgt-2` and `xgt-3` .

The common solution is `xgt-2` .

**Therefore, the solutions for the given inequaility are x <-3 or x>-2.**

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