algebraic equations?

Question

if ( mx + 7) ( 5x + n ) = px^2 +15x +14, find m( n+p )

Answer 1

Let's multiply through:
5m * x² + 35x + mnx + 7n = px² + 15x + 14.

Trying to match up your coefficients:
5m = p
(35 + mn) = 15
7n = 14

So I'd assume n = 2

From the middle equation:
(35 + 2m) = 15
2m = -20
m = -10

So we have m = -10.

Finally
5m = p
5(-10) = p
p = -50

With:
m = -10
n = 2
p = -50

You can solve:
m( n + p )
-10(2 - 50)
-10( -48 )
= 480