Solve 1/8[(x-2)(x-3)]-15/4=1/4[(x^2-6x)-1/2x(x+1)]-1

$$\frac { 1 } { 8 } [ ( x - 2 ) ( x - 3 ) ] - \frac { 15 } { 4 } = \frac { 1 } { 4 } [ ( x ^ { 2 } - 6 x ) - \frac { 1 } { 2 } x ( x + 1 ) ] - 1$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{8} by x-2.

$$\left(\frac{1}{8}x-\frac{1}{4}\right)\left(x-3\right)-\frac{15}{4}=\frac{1}{4}\left(x^{2}-6x-\frac{1}{2}x\left(x+1\right)\right)-1$$

Use the distributive property to multiply \frac{1}{8}x-\frac{1}{4} by x-3 and combine like terms.

$$\frac{1}{8}x^{2}-\frac{5}{8}x+\frac{3}{4}-\frac{15}{4}=\frac{1}{4}\left(x^{2}-6x-\frac{1}{2}x\left(x+1\right)\right)-1$$

Subtract \frac{15}{4} from \frac{3}{4} to get -3.

$$\frac{1}{8}x^{2}-\frac{5}{8}x-3=\frac{1}{4}\left(x^{2}-6x-\frac{1}{2}x\left(x+1\right)\right)-1$$

Subtract \frac{1}{4}\left(x^{2}-6x-\frac{1}{2}x\left(x+1\right)\right) from both sides.

$$\frac{1}{8}x^{2}-\frac{5}{8}x-3-\frac{1}{4}\left(x^{2}-6x-\frac{1}{2}x\left(x+1\right)\right)=-1$$

Use the distributive property to multiply -\frac{1}{2}x by x+1.

$$\frac{1}{8}x^{2}-\frac{5}{8}x-3-\frac{1}{4}\left(x^{2}-6x-\frac{1}{2}x^{2}-\frac{1}{2}x\right)=-1$$

Combine x^{2} and -\frac{1}{2}x^{2} to get \frac{1}{2}x^{2}.

$$\frac{1}{8}x^{2}-\frac{5}{8}x-3-\frac{1}{4}\left(\frac{1}{2}x^{2}-6x-\frac{1}{2}x\right)=-1$$

Combine -6x and -\frac{1}{2}x to get -\frac{13}{2}x.

$$\frac{1}{8}x^{2}-\frac{5}{8}x-3-\frac{1}{4}\left(\frac{1}{2}x^{2}-\frac{13}{2}x\right)=-1$$

Use the distributive property to multiply -\frac{1}{4} by \frac{1}{2}x^{2}-\frac{13}{2}x.

$$\frac{1}{8}x^{2}-\frac{5}{8}x-3-\frac{1}{8}x^{2}+\frac{13}{8}x=-1$$

Combine \frac{1}{8}x^{2} and -\frac{1}{8}x^{2} to get 0.

$$-\frac{5}{8}x-3+\frac{13}{8}x=-1$$

Combine -\frac{5}{8}x and \frac{13}{8}x to get x.

$$x-3=-1$$

Add 3 to both sides.

$$x=-1+3$$

Add -1 and 3 to get 2.

$$x=2$$