If 8 is added to twice a number and this sum multiplied by 6, the result is the same as if the number is multiplied by 7 and 13 is added to the product. what is the number

Let n represent the number.

(8 +2n)×6 = 7n +13 . . . . . the problem statement translated to symbols

48 +12n = 7n +13 . . . . . . eliminate parentheses

35 +5n = 0 . . . . . . . . . . . subtract the right side

7 + n = 0 . . . . . . . . . . . . . divide by the coefficient of n

n = -7 . . . . . . . . . . . . . . . add the opposite of the constant

The number is -7.

Check

8 is added to twice the number: 2·(-7) +8 = -14+8 = -6

and this sum is multiplied by 6: -6·6 = -36.

This result is the same as if the number is multiplied by 7: -7·7 = -49

and 13 is added to the product: -49+13 = -36.

Indeed, we see both results are -36, the same.

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

⭐⭐

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.