Solve for q x^2+px+q=(x-13)(x+1)

$x^{2} + p x + q = (x - 13) (x + 1)$

Step 1

Simplify $(x - 13) (x + 1)$ .

Rewrite.

$x^{2} + p x + q = 0 + 0 + (x - 13) (x + 1)$

Simplify by adding zeros.

$x^{2} + p x + q = (x - 13) (x + 1)$

Expand $(x - 13) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$x^{2} + p x + q = x (x + 1) - 13 (x + 1)$

Apply the distributive property.

$x^{2} + p x + q = x \cdot x + x \cdot 1 - 13 (x + 1)$

Apply the distributive property.

$x^{2} + p x + q = x \cdot x + x \cdot 1 - 13 x - 13 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + p x + q = x^{2} + x \cdot 1 - 13 x - 13 \cdot 1$

Multiply $x$ by $1$ .

$x^{2} + p x + q = x^{2} + x - 13 x - 13 \cdot 1$

Multiply $- 13$ by $1$ .

$x^{2} + p x + q = x^{2} + x - 13 x - 13$

Subtract $13 x$ from $x$ .

$x^{2} + p x + q = x^{2} - 12 x - 13$

Step 2

Move all terms not containing $q$ to the right side of the equation.

Subtract $x^{2}$ from both sides of the equation.

$p x + q = x^{2} - 12 x - 13 - x^{2}$

Subtract $p x$ from both sides of the equation.

$q = x^{2} - 12 x - 13 - x^{2} - p x$

Combine the opposite terms in $x^{2} - 12 x - 13 - x^{2} - p x$ .

Subtract $x^{2}$ from $x^{2}$ .

$q = - 12 x - 13 + 0 - p x$

Add $- 12 x - 13$ and $0$ .

$q = - 12 x - 13 - p x$