Precalculus Examples

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

Step 1

Subtract $15 x$ from $2 x$ .

$x^{2} - 13 x = x$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$x^{2} - 13 x - x = 0$

Step 2.2

Subtract $x$ from $- 13 x$ .

$x^{2} - 14 x = 0$

Step 3

Factor $x$ out of $x^{2} - 14 x$ .

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Step 3.1

Factor $x$ out of $x^{2}$ .

$x \cdot x - 14 x = 0$

Step 3.2

Factor $x$ out of $- 14 x$ .

$x \cdot x + x \cdot - 14 = 0$

Step 3.3

Factor $x$ out of $x \cdot x + x \cdot - 14$ .

$x (x - 14) = 0$

Step 4

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

$x = 0$

$x - 14 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x - 14$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 14$ equal to $0$ .

$x - 14 = 0$

Step 6.2

Add $14$ to both sides of the equation.

$x = 14$

Step 7

The final solution is all the values that make $x (x - 14) = 0$ true.

$x = 0, 14$