Solve for x 2(3x+4y)=4x+12y

$2 (3 x + 4 y) = 4 x + 12 y$

Step 1

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

Rewrite.

$0 + 0 + 2 (3 x + 4 y) = 4 x + 12 y$

Simplify by adding zeros.

$2 (3 x + 4 y) = 4 x + 12 y$

Apply the distributive property.

$2 (3 x) + 2 (4 y) = 4 x + 12 y$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 (4 y) = 4 x + 12 y$

Multiply $4$ by $2$ .

$6 x + 8 y = 4 x + 12 y$

Step 2

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

Subtract $4 x$ from both sides of the equation.

$6 x + 8 y - 4 x = 12 y$

Subtract $4 x$ from $6 x$ .

$2 x + 8 y = 12 y$

Step 3

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

Subtract $8 y$ from both sides of the equation.

$2 x = 12 y - 8 y$

Subtract $8 y$ from $12 y$ .

$2 x = 4 y$

Step 4

Divide each term in $2 x = 4 y$ by $2$ and simplify.

Divide each term in $2 x = 4 y$ by $2$ .

$\frac{2 x}{2} = \frac{4 y}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4 y}{2}$

Divide $x$ by $1$ .

$x = \frac{4 y}{2}$

Simplify the right side.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 y$ .

$x = \frac{2 (2 y)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{2 (2 y)}{2 (1)}$

Cancel the common factor.

$x = \frac{2 (2 y)}{2 \cdot 1}$

Rewrite the expression.

$x = \frac{2 y}{1}$

Divide $2 y$ by $1$ .

$x = 2 y$

Solve for x 2(3x+4y)=4x+12y

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