Solve for x (0.5x+1.2)-(3.6-4.5x)=(4.8-0.3x)+(10.5x+0.6)

$(0.5 x + 1.2) - (3.6 - 4.5 x) = (4.8 - 0.3 x) + (10.5 x + 0.6)$

Simplify $0.5 x + 1.2 - (3.6 - 4.5 x)$ .

Simplify each term.

Apply the distributive property.

$0.5 x + 1.2 - 1 \cdot 3.6 - (- 4.5 x) = 4.8 - 0.3 x + 10.5 x + 0.6$

Multiply $- 1$ by $3.6$ .

$0.5 x + 1.2 - 3.6 - (- 4.5 x) = 4.8 - 0.3 x + 10.5 x + 0.6$

Multiply $- 4.5$ by $- 1$ .

$0.5 x + 1.2 - 3.6 + 4.5 x = 4.8 - 0.3 x + 10.5 x + 0.6$

Simplify by adding terms.

Add $0.5 x$ and $4.5 x$ .

$5 x + 1.2 - 3.6 = 4.8 - 0.3 x + 10.5 x + 0.6$

Subtract $3.6$ from $1.2$ .

$5 x - 2.4 = 4.8 - 0.3 x + 10.5 x + 0.6$

Simplify $4.8 - 0.3 x + 10.5 x + 0.6$ .

Add $4.8$ and $0.6$ .

$5 x - 2.4 = - 0.3 x + 10.5 x + 5.4$

Add $- 0.3 x$ and $10.5 x$ .

$5 x - 2.4 = 10.2 x + 5.4$

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

Subtract $10.2 x$ from both sides of the equation.

$5 x - 2.4 - 10.2 x = 5.4$

Subtract $10.2 x$ from $5 x$ .

$- 5.2 x - 2.4 = 5.4$

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

Add $2.4$ to both sides of the equation.

$- 5.2 x = 5.4 + 2.4$

Add $5.4$ and $2.4$ .

$- 5.2 x = 7.8$

Divide each term in $- 5.2 x = 7.8$ by $- 5.2$ and simplify.

Divide each term in $- 5.2 x = 7.8$ by $- 5.2$ .

$\frac{- 5.2 x}{- 5.2} = \frac{7.8}{- 5.2}$

Simplify the left side.

Cancel the common factor of $- 5.2$ .

Cancel the common factor.

$\frac{- 5.2 x}{- 5.2} = \frac{7.8}{- 5.2}$

Divide $x$ by $1$ .

$x = \frac{7.8}{- 5.2}$

Simplify the right side.

Divide $7.8$ by $- 5.2$ .

$x = - 1.5$