Solve by Factoring 0=x^2-15x+36

$0 = x^{2} - 15 x + 36$

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

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

$- x^{2} = - 15 x + 36$

Add $15 x$ to both sides of the equation.

$- x^{2} + 15 x = 36$

Subtract $36$ from both sides of the equation.

$- x^{2} + 15 x - 36 = 0$

Factor by grouping.

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 $a \cdot c = - 1 \cdot - 36 = 36$ and whose sum is $b = 15$ .

Factor $15$ out of $15 x$ .

$- x^{2} + 15 (x) - 36 = 0$

Rewrite $15$ as $3$ plus $12$

$- x^{2} + (3 + 12) x - 36 = 0$

Apply the distributive property.

$- x^{2} + 3 x + 12 x - 36 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(- x^{2} + 3 x) + 12 x - 36 = 0$

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

$x (- x + 3) - 12 (- x + 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $- x + 3$ .

$(- x + 3) (x - 12) = 0$

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

$- x + 3 = 0$

$x - 12 = 0$

Set $- x + 3$ equal to $0$ and solve for $x$ .

Set $- x + 3$ equal to $0$ .

$- x + 3 = 0$

Solve $- x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$- x = - 3$

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x = 3$

Set $x - 12$ equal to $0$ and solve for $x$ .

Set $x - 12$ equal to $0$ .

$x - 12 = 0$

Add $12$ to both sides of the equation.

$x = 12$

The final solution is all the values that make $(- x + 3) (x - 12) = 0$ true.

$x = 3, 12$

Solve by Factoring 0=x^2-15x+36

Related Questions

Support LCMGCF.com by disabling your adblocker.