Solve for x 3x(2x+4)=2(3x^2+48)

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

Step 1

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

Start simplifying.

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

Simplify by multiplying through.

Apply the distributive property.

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $4$ by $3$ .

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

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $2$ .

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

Step 2

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

Apply the distributive property.

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

Multiply.

Multiply $3$ by $2$ .

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

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.

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

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

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

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

$12 x + 0 = 96$

Add $12 x$ and $0$ .

$12 x = 96$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $96$ by $12$ .

$x = 8$

Solve for x 3x(2x+4)=2(3x^2+48)

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