Algebra Examples

$\frac{15 (x - 3)}{5} = 3 (2 x - 3)$

Step 1

Cancel the common factor of $15$ and $5$ .

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Step 1.1

Factor $5$ out of $15 (x - 3)$ .

$\frac{5 (3 (x - 3))}{5} = 3 (2 x - 3)$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $5$ .

$\frac{5 (3 (x - 3))}{5 (1)} = 3 (2 x - 3)$

Step 1.2.2

Cancel the common factor.

$\frac{5 (3 (x - 3))}{5 \cdot 1} = 3 (2 x - 3)$

Step 1.2.3

Rewrite the expression.

$\frac{3 (x - 3)}{1} = 3 (2 x - 3)$

Step 1.2.4

Divide $3 (x - 3)$ by $1$ .

$3 (x - 3) = 3 (2 x - 3)$

$3 (x - 3) = 3 (2 x - 3)$

$3 (x - 3) = 3 (2 x - 3)$

Step 2

Solve for $x$ .

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Step 2.1

Simplify $3 (x - 3)$ .

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Step 2.1.1

Rewrite.

$0 + 0 + 3 (x - 3) = 3 (2 x - 3)$

Step 2.1.2

Simplify by adding zeros.

$3 (x - 3) = 3 (2 x - 3)$

Step 2.1.3

Apply the distributive property.

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

Step 2.1.4

Multiply $3$ by $- 3$ .

$3 x - 9 = 3 (2 x - 3)$

$3 x - 9 = 3 (2 x - 3)$

Step 2.2

Simplify $3 (2 x - 3)$ .

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Step 2.2.1

Apply the distributive property.

$3 x - 9 = 3 (2 x) + 3 \cdot - 3$

Step 2.2.2

Multiply.

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Step 2.2.2.1

Multiply $2$ by $3$ .

$3 x - 9 = 6 x + 3 \cdot - 3$

Step 2.2.2.2

Multiply $3$ by $- 3$ .

$3 x - 9 = 6 x - 9$

$3 x - 9 = 6 x - 9$

$3 x - 9 = 6 x - 9$

Step 2.3

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

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Step 2.3.1

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

$3 x - 9 - 6 x = - 9$

Step 2.3.2

Subtract $6 x$ from $3 x$ .

$- 3 x - 9 = - 9$

$- 3 x - 9 = - 9$

Step 2.4

Move all terms not containing $x$ to the right side of the equation.

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Step 2.4.1

Add $9$ to both sides of the equation.

$- 3 x = - 9 + 9$

Step 2.4.2

Add $- 9$ and $9$ .

$- 3 x = 0$

$- 3 x = 0$

Step 2.5

Divide each term in $- 3 x = 0$ by $- 3$ and simplify.

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Step 2.5.1

Divide each term in $- 3 x = 0$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{0}{- 3}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $- 3$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{0}{- 3}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 3}$

$x = \frac{0}{- 3}$

$x = \frac{0}{- 3}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Divide $0$ by $- 3$ .

$x = 0$

$x = 0$

$x = 0$

$x = 0$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$