Pre-Algebra Examples

$15 x = 10 x + 12 x^{2}$

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.

$10 x + 12 x^{2} = 15 x$

Step 2

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

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Step 2.1

Subtract $15 x$ from both sides of the equation.

$10 x + 12 x^{2} - 15 x = 0$

Step 2.2

Subtract $15 x$ from $10 x$ .

$12 x^{2} - 5 x = 0$

Step 3

Factor $x$ out of $12 x^{2} - 5 x$ .

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Step 3.1

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

$x (12 x) - 5 x = 0$

Step 3.2

Factor $x$ out of $- 5 x$ .

$x (12 x) + x \cdot - 5 = 0$

Step 3.3

Factor $x$ out of $x (12 x) + x \cdot - 5$ .

$x (12 x - 5) = 0$

Step 4

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

$x = 0$

$12 x - 5 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $12 x - 5$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $12 x - 5$ equal to $0$ .

$12 x - 5 = 0$

Step 6.2

Solve $12 x - 5 = 0$ for $x$ .

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Step 6.2.1

Add $5$ to both sides of the equation.

$12 x = 5$

Step 6.2.2

Divide each term in $12 x = 5$ by $12$ and simplify.

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Step 6.2.2.1

Divide each term in $12 x = 5$ by $12$ .

$\frac{12 x}{12} = \frac{5}{12}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $12$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{5}{12}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{12}$

Step 7

The final solution is all the values that make $x (12 x - 5) = 0$ true.

$x = 0, \frac{5}{12}$