Find a,b,c (x-6)(x-9)=0

$(x - 6) (x - 9) = 0$

Step 1

Simplify the left side.

Simplify $(x - 6) (x - 9)$ .

Expand $(x - 6) (x - 9)$ using the FOIL Method.

Apply the distributive property.

$x (x - 9) - 6 (x - 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 9 - 6 (x - 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 9 - 6 x - 6 \cdot - 9 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 9 - 6 x - 6 \cdot - 9 = 0$

Move $- 9$ to the left of $x$ .

$x^{2} - 9 \cdot x - 6 x - 6 \cdot - 9 = 0$

Multiply $- 6$ by $- 9$ .

$x^{2} - 9 x - 6 x + 54 = 0$

Subtract $6 x$ from $- 9 x$ .

$x^{2} - 15 x + 54 = 0$

Step 2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Step 3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 1$ , $b = - 15$ , $c = 54$