Solve 15=1/2*((6+2)(x-2)-(0-2)(-1-2))

$$15= \frac{ 1 }{ 2 } \times ((6+2)(x-2)-(0-2)(-1-2))$$

Solve for x

$$x = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

Steps for Solving Linear Equation

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$15\times 2=\left(6+2\right)\left(x-2\right)-\left(0-2\right)\left(-1-2\right)$$

Multiply 15 and 2 to get 30.

$$30=\left(6+2\right)\left(x-2\right)-\left(0-2\right)\left(-1-2\right)$$

Add 6 and 2 to get 8.

$$30=8\left(x-2\right)-\left(0-2\right)\left(-1-2\right)$$

Use the distributive property to multiply 8 by x-2.

$$30=8x-16-\left(0-2\right)\left(-1-2\right)$$

Subtract 2 from 0 to get -2.

$$30=8x-16-\left(-2\left(-1-2\right)\right)$$

Subtract 2 from -1 to get -3.

$$30=8x-16-\left(-2\left(-3\right)\right)$$

Multiply -2 and -3 to get 6.

$$30=8x-16-6$$

Subtract 6 from -16 to get -22.

$$30=8x-22$$

Swap sides so that all variable terms are on the left hand side.

$$8x-22=30$$

Add 22 to both sides.

$$8x=30+22$$

Add 30 and 22 to get 52.

$$8x=52$$

Divide both sides by 8.

$$x=\frac{52}{8}$$

Reduce the fraction \frac{52}{8} to lowest terms by extracting and canceling out 4.

$$x=\frac{13}{2}$$