Solve for x (x-3)(x+4)=x^2+4

$(x - 3) (x + 4) = x^{2} + 4$

Simplify $(x - 3) (x + 4)$ .

Rewrite.

$0 + 0 + (x - 3) (x + 4) = x^{2} + 4$

Simplify by adding zeros.

$(x - 3) (x + 4) = x^{2} + 4$

Expand $(x - 3) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$x (x + 4) - 3 (x + 4) = x^{2} + 4$

Apply the distributive property.

$x \cdot x + x \cdot 4 - 3 (x + 4) = x^{2} + 4$

Apply the distributive property.

$x \cdot x + x \cdot 4 - 3 x - 3 \cdot 4 = x^{2} + 4$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 4 - 3 x - 3 \cdot 4 = x^{2} + 4$

Move $4$ to the left of $x$ .

$x^{2} + 4 \cdot x - 3 x - 3 \cdot 4 = x^{2} + 4$

Multiply $- 3$ by $4$ .

$x^{2} + 4 x - 3 x - 12 = x^{2} + 4$

Subtract $3 x$ from $4 x$ .

$x^{2} + x - 12 = x^{2} + 4$

Move all terms containing $x$ to the left side of the equation.

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

$x^{2} + x - 12 - x^{2} = 4$

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

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

$x - 12 + 0 = 4$

Add $x - 12$ and $0$ .

$x - 12 = 4$

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

Add $12$ to both sides of the equation.

$x = 4 + 12$

Add $4$ and $12$ .

$x = 16$