Solve for x (x-9)(x+2)=x^2+3

$(x - 9) (x + 2) = x^{2} + 3$

Simplify $(x - 9) (x + 2)$ .

Rewrite.

$0 + 0 + (x - 9) (x + 2) = x^{2} + 3$

Simplify by adding zeros.

$(x - 9) (x + 2) = x^{2} + 3$

Expand $(x - 9) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$x (x + 2) - 9 (x + 2) = x^{2} + 3$

Apply the distributive property.

$x \cdot x + x \cdot 2 - 9 (x + 2) = x^{2} + 3$

Apply the distributive property.

$x \cdot x + x \cdot 2 - 9 x - 9 \cdot 2 = x^{2} + 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 2 - 9 x - 9 \cdot 2 = x^{2} + 3$

Move $2$ to the left of $x$ .

$x^{2} + 2 \cdot x - 9 x - 9 \cdot 2 = x^{2} + 3$

Multiply $- 9$ by $2$ .

$x^{2} + 2 x - 9 x - 18 = x^{2} + 3$

Subtract $9 x$ from $2 x$ .

$x^{2} - 7 x - 18 = x^{2} + 3$

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

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

$x^{2} - 7 x - 18 - x^{2} = 3$

Combine the opposite terms in $x^{2} - 7 x - 18 - x^{2}$ .

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

$- 7 x - 18 + 0 = 3$

Add $- 7 x - 18$ and $0$ .

$- 7 x - 18 = 3$

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

Add $18$ to both sides of the equation.

$- 7 x = 3 + 18$

Add $3$ and $18$ .

$- 7 x = 21$

Divide each term in $- 7 x = 21$ by $- 7$ and simplify.

Divide each term in $- 7 x = 21$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{21}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{21}{- 7}$

Divide $x$ by $1$ .

$x = \frac{21}{- 7}$

Simplify the right side.

Divide $21$ by $- 7$ .

$x = - 3$

Solve for x (x-9)(x+2)=x^2+3

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