Pre-Algebra Examples

$3 x = 5 x^{2} + 13 x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$5 x^{2} + 13 x = 3 x$

Step 2

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

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Step 2.1

Subtract $3 x$ from both sides of the equation.

$5 x^{2} + 13 x - 3 x = 0$

Step 2.2

Subtract $3 x$ from $13 x$ .

$5 x^{2} + 10 x = 0$

Step 3

Factor $5 x$ out of $5 x^{2} + 10 x$ .

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Step 3.1

Factor $5 x$ out of $5 x^{2}$ .

$5 x (x) + 10 x = 0$

Step 3.2

Factor $5 x$ out of $10 x$ .

$5 x (x) + 5 x (2) = 0$

Step 3.3

Factor $5 x$ out of $5 x (x) + 5 x (2)$ .

$5 x (x + 2) = 0$

Step 4

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

$x = 0$

$x + 2 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

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

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Step 6.1

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

$x + 2 = 0$

Step 6.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

The final solution is all the values that make $5 x (x + 2) = 0$ true.

$x = 0, - 2$