Solve by Factoring 18=6x+x(x-13)

$18 = 6 x + x (x - 13)$

Step 1

Move all the expressions to the left side of the equation.

Subtract $6 x$ from both sides of the equation.

$18 - 6 x = x (x - 13)$

Subtract $x (x - 13)$ from both sides of the equation.

$18 - 6 x - x (x - 13) = 0$

Step 2

Simplify $18 - 6 x - x (x - 13)$ .

Simplify each term.

Apply the distributive property.

$18 - 6 x - x \cdot x - x \cdot - 13 = 0$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$18 - 6 x - (x \cdot x) - x \cdot - 13 = 0$

Multiply $x$ by $x$ .

$18 - 6 x - x^{2} - x \cdot - 13 = 0$

Multiply $- 13$ by $- 1$ .

$18 - 6 x - x^{2} + 13 x = 0$

Add $- 6 x$ and $13 x$ .

$18 - x^{2} + 7 x = 0$

Step 3

Factor by grouping.

Reorder terms.

$- x^{2} + 7 x + 18 = 0$

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 1 \cdot 18 = - 18$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$- x^{2} + 7 (x) + 18 = 0$

Rewrite $7$ as $- 2$ plus $9$

$- x^{2} + (- 2 + 9) x + 18 = 0$

Apply the distributive property.

$- x^{2} - 2 x + 9 x + 18 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- x^{2} - 2 x) + 9 x + 18 = 0$

Factor out the greatest common factor (GCF) from each group.

$x (- x - 2) - 9 (- x - 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $- x - 2$ .

$(- x - 2) (x - 9) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$- x - 2 = 0$

$x - 9 = 0$

Step 5

Set $- x - 2$ equal to $0$ and solve for $x$ .

Set $- x - 2$ equal to $0$ .

$- x - 2 = 0$

Solve $- x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$- x = 2$

Divide each term in $- x = 2$ by $- 1$ and simplify.

Divide each term in $- x = 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$x = - 2$

Step 6

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Step 7

The final solution is all the values that make $(- x - 2) (x - 9) = 0$ true.

$x = - 2, 9$

Solve by Factoring 18=6x+x(x-13)

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