Algebra Examples

$3 x (2 x + 4) = 2 (3 x^{2} + 48)$

Step 1

Simplify $3 x (2 x + 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 x (2 x + 4) = 2 (3 x^{2} + 48)$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$3 x (2 x) + 3 x \cdot 4 = 2 (3 x^{2} + 48)$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x + 3 x \cdot 4 = 2 (3 x^{2} + 48)$

Step 1.2.2.2

Multiply $4$ by $3$ .

$3 \cdot 2 x \cdot x + 12 x = 2 (3 x^{2} + 48)$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $x$ .

$3 \cdot 2 (x \cdot x) + 12 x = 2 (3 x^{2} + 48)$

Step 1.3.1.2

Multiply $x$ by $x$ .

$3 \cdot 2 x^{2} + 12 x = 2 (3 x^{2} + 48)$

Step 1.3.2

Multiply $3$ by $2$ .

$6 x^{2} + 12 x = 2 (3 x^{2} + 48)$

Step 2

Simplify $2 (3 x^{2} + 48)$ .

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Step 2.1

Apply the distributive property.

$6 x^{2} + 12 x = 2 (3 x^{2}) + 2 \cdot 48$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $3$ by $2$ .

$6 x^{2} + 12 x = 6 x^{2} + 2 \cdot 48$

Step 2.2.2

Multiply $2$ by $48$ .

$6 x^{2} + 12 x = 6 x^{2} + 96$

Step 3

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

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Step 3.1

Subtract $6 x^{2}$ from both sides of the equation.

$6 x^{2} + 12 x - 6 x^{2} = 96$

Step 3.2

Combine the opposite terms in $6 x^{2} + 12 x - 6 x^{2}$ .

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Step 3.2.1

Subtract $6 x^{2}$ from $6 x^{2}$ .

$12 x + 0 = 96$

Step 3.2.2

Add $12 x$ and $0$ .

$12 x = 96$

Step 4

Divide each term in $12 x = 96$ by $12$ and simplify.

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Step 4.1

Divide each term in $12 x = 96$ by $12$ .

$\frac{12 x}{12} = \frac{96}{12}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $12$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{96}{12}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{96}{12}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $96$ by $12$ .

$x = 8$