X (x-3) = 28 use factoring to solve the polynomial equation

x = - 4, x = 7

Step-by-step explanation:

Given

x (x - 3) = 28 ← distribute left side

x² - 3x = 28 ← subtract 28 from both sides

x² - 3x - 28 = 0 ← in standard form

To factor the quadratic

Consider the factors of the constant term ( - 28) which sum to give the coefficient of the x - term ( - 3)

The factors are - 7 and + 4, since

- 7 * 4 = - 28 and - 7 + 4 = - 3, hence

(x - 7) (x + 4) = 0

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 4 = 0 ⇒ x = - 4