Pre-Algebra Examples

$3 x^{2} + 6 x = 24 x$

Step 1

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

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Step 1.1

Subtract $24 x$ from both sides of the equation.

$3 x^{2} + 6 x - 24 x = 0$

Step 1.2

Subtract $24 x$ from $6 x$ .

$3 x^{2} - 18 x = 0$

Step 2

Factor $3 x$ out of $3 x^{2} - 18 x$ .

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Step 2.1

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

$3 x (x) - 18 x = 0$

Step 2.2

Factor $3 x$ out of $- 18 x$ .

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

Step 2.3

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

$3 x (x - 6) = 0$

Step 3

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

$x = 0$

$x - 6 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x - 6$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 5.2

Add $6$ to both sides of the equation.

$x = 6$

Step 6

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

$x = 0, 6$