Parallel Tangents to Cubic Graph

[flyinghigh]

Homework Statement

I have the graph of a function f(x)=(x+1)(x+4)(x+6). I've found the tangent at x=-6, the equation of which is y=10x+60. I then need to algebraically find the equation of another tangent on the curve which is parallel to the first.

Homework Equations

No idea.

The Attempt at a Solution

Since I'm graphing this on Autograph I've managed to find a point where the tangent is parallel to the first, but since this can be done without the computer program I'm really interested to know how it's done. So yeah, I know that the tangent I'm trying to find will have a gradient of 10 but that's about it...

Any help would be great,
flyinghigh

 

[Redbelly98]

Okay, you know you're looking for a tangent line with a slope of 10.

Can you write an equation for the slope of the tangent (as a function of x), and set that equal to 10?