Algebra Examples

$\frac{4 x}{6 x + 4} = \frac{x}{25}$

Step 1

Cancel the common factor of $4$ and $6 x + 4$ .

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Step 1.1

Factor $2$ out of $4 x$ .

$\frac{2 (2 x)}{6 x + 4} = \frac{x}{25}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $6 x$ .

$\frac{2 (2 x)}{2 (3 x) + 4} = \frac{x}{25}$

Step 1.2.2

Factor $2$ out of $4$ .

$\frac{2 (2 x)}{2 (3 x) + 2 (2)} = \frac{x}{25}$

Step 1.2.3

Factor $2$ out of $2 (3 x) + 2 (2)$ .

$\frac{2 (2 x)}{2 (3 x + 2)} = \frac{x}{25}$

Step 1.2.4

Cancel the common factor.

$\frac{2 (2 x)}{2 (3 x + 2)} = \frac{x}{25}$

Step 1.2.5

Rewrite the expression.

$\frac{2 x}{3 x + 2} = \frac{x}{25}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$2 x \cdot 25 = (3 x + 2) x$

Step 3

Solve the equation for $x$ .

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Step 3.1

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

$(3 x + 2) x = 2 x \cdot 25$

Step 3.2

Simplify $(3 x + 2) x$ .

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Step 3.2.1

Rewrite.

$0 + 0 + (3 x + 2) x = 2 x \cdot 25$

Step 3.2.2

Simplify by adding zeros.

$(3 x + 2) x = 2 x \cdot 25$

Step 3.2.3

Apply the distributive property.

$3 x \cdot x + 2 x = 2 x \cdot 25$

Step 3.2.4

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

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Step 3.2.4.1

Move $x$ .

$3 (x \cdot x) + 2 x = 2 x \cdot 25$

Step 3.2.4.2

Multiply $x$ by $x$ .

$3 x^{2} + 2 x = 2 x \cdot 25$

Step 3.3

Multiply $25$ by $2$ .

$3 x^{2} + 2 x = 50 x$

Step 3.4

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

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Step 3.4.1

Subtract $50 x$ from both sides of the equation.

$3 x^{2} + 2 x - 50 x = 0$

Step 3.4.2

Subtract $50 x$ from $2 x$ .

$3 x^{2} - 48 x = 0$

Step 3.5

Factor $3 x$ out of $3 x^{2} - 48 x$ .

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Step 3.5.1

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

$3 x (x) - 48 x = 0$

Step 3.5.2

Factor $3 x$ out of $- 48 x$ .

$3 x (x) + 3 x (- 16) = 0$

Step 3.5.3

Factor $3 x$ out of $3 x (x) + 3 x (- 16)$ .

$3 x (x - 16) = 0$

Step 3.6

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

$x = 0$

$x - 16 = 0$

Step 3.7

Set $x$ equal to $0$ .

$x = 0$

Step 3.8

Set $x - 16$ equal to $0$ and solve for $x$ .

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Step 3.8.1

Set $x - 16$ equal to $0$ .

$x - 16 = 0$

Step 3.8.2

Add $16$ to both sides of the equation.

$x = 16$

Step 3.9

The final solution is all the values that make $3 x (x - 16) = 0$ true.

$x = 0, 16$