Find the Equation Given the Roots x=-3 , x=7

$x = - 3$ , $x = 7$

Step 1

Since the roots of an equation are the points where the solution is $0$ , set each root as a factor of the equation that equals $0$ .

$(x - (- 3)) (x - 7) = 0$

Step 2

Simplify.

Expand $(x + 3) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$x (x - 7) + 3 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 3 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 3 x + 3 \cdot - 7 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 7 + 3 x + 3 \cdot - 7 = 0$

Move $- 7$ to the left of $x$ .

$x^{2} - 7 \cdot x + 3 x + 3 \cdot - 7 = 0$

Multiply $3$ by $- 7$ .

$x^{2} - 7 x + 3 x - 21 = 0$

Add $- 7 x$ and $3 x$ .

$x^{2} - 4 x - 21 = 0$