Pre-Algebra Examples

$6 x = x (8 x + 25)$

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.

$x (8 x + 25) = 6 x$

Step 2

Simplify $x (8 x + 25)$ .

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Step 2.1

Rewrite.

$0 + 0 + x (8 x + 25) = 6 x$

Step 2.2

Simplify by multiplying through.

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Step 2.2.1

Apply the distributive property.

$x (8 x) + x \cdot 25 = 6 x$

Step 2.2.2

Reorder.

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Step 2.2.2.1

Rewrite using the commutative property of multiplication.

$8 x \cdot x + x \cdot 25 = 6 x$

Step 2.2.2.2

Move $25$ to the left of $x$ .

$8 x \cdot x + 25 \cdot x = 6 x$

Step 2.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.3.1

Move $x$ .

$8 (x \cdot x) + 25 \cdot x = 6 x$

Step 2.3.2

Multiply $x$ by $x$ .

$8 x^{2} + 25 \cdot x = 6 x$

$8 x^{2} + 25 x = 6 x$

Step 3

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

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Step 3.1

Subtract $6 x$ from both sides of the equation.

$8 x^{2} + 25 x - 6 x = 0$

Step 3.2

Subtract $6 x$ from $25 x$ .

$8 x^{2} + 19 x = 0$

Step 4

Factor $x$ out of $8 x^{2} + 19 x$ .

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Step 4.1

Factor $x$ out of $8 x^{2}$ .

$x (8 x) + 19 x = 0$

Step 4.2

Factor $x$ out of $19 x$ .

$x (8 x) + x \cdot 19 = 0$

Step 4.3

Factor $x$ out of $x (8 x) + x \cdot 19$ .

$x (8 x + 19) = 0$

Step 5

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

$x = 0$

$8 x + 19 = 0$

Step 6

Set $x$ equal to $0$ .

$x = 0$

Step 7

Set $8 x + 19$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $8 x + 19$ equal to $0$ .

$8 x + 19 = 0$

Step 7.2

Solve $8 x + 19 = 0$ for $x$ .

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Step 7.2.1

Subtract $19$ from both sides of the equation.

$8 x = - 19$

Step 7.2.2

Divide each term in $8 x = - 19$ by $8$ and simplify.

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Step 7.2.2.1

Divide each term in $8 x = - 19$ by $8$ .

$\frac{8 x}{8} = \frac{- 19}{8}$

Step 7.2.2.2

Simplify the left side.

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Step 7.2.2.2.1

Cancel the common factor of $8$ .

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Step 7.2.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 19}{8}$

Step 7.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 19}{8}$

Step 7.2.2.3

Simplify the right side.

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Step 7.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{19}{8}$

Step 8

The final solution is all the values that make $x (8 x + 19) = 0$ true.

$x = 0, - \frac{19}{8}$