Pre-Algebra Examples

$3 x^{2} - x = - 13 x$

Step 1

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

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Step 1.1

Add $13 x$ to both sides of the equation.

$3 x^{2} - x + 13 x = 0$

Step 1.2

Add $- x$ and $13 x$ .

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

Step 2

Factor $3 x$ out of $3 x^{2} + 12 x$ .

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Step 2.1

Factor $3 x$ out of $3 x^{2}$ .

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

Step 2.2

Factor $3 x$ out of $12 x$ .

$3 x (x) + 3 x (4) = 0$

Step 2.3

Factor $3 x$ out of $3 x (x) + 3 x (4)$ .

$3 x (x + 4) = 0$

Step 3

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

$x = 0$

$x + 4 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x + 4$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Step 5.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 6

The final solution is all the values that make $3 x (x + 4) = 0$ true.

$x = 0, - 4$