Precalculus Examples

$6 x^{2} - 15 x = 3 x$

Step 1

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

$6 x^{2} - 15 x - 3 x = 0$

Step 2

Subtract $3 x$ from $- 15 x$ .

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

Step 3

Factor $6 x$ out of $6 x^{2} - 18 x$ .

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Step 3.1

Factor $6 x$ out of $6 x^{2}$ .

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

Step 3.2

Factor $6 x$ out of $- 18 x$ .

$6 x (x) + 6 x (- 3) = 0$

Step 3.3

Factor $6 x$ out of $6 x (x) + 6 x (- 3)$ .

$6 x (x - 3) = 0$

Step 4

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

$x = 0$

$x - 3 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

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

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Step 6.1

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

$x - 3 = 0$

Step 6.2

Add $3$ to both sides of the equation.

$x = 3$

Step 7

The final solution is all the values that make $6 x (x - 3) = 0$ true.

$x = 0, 3$