Solve (2x-1)(x+2)-0.5x=(x-4)(2x+3)-5

$$(2x-1)(x+2)-0.5x=(x-4)(2x+3)-5$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by x+2 and combine like terms.

$$2x^{2}+3x-2-0.5x=\left(x-4\right)\left(2x+3\right)-5$$

Combine 3x and -0.5x to get 2.5x.

$$2x^{2}+2.5x-2=\left(x-4\right)\left(2x+3\right)-5$$

Use the distributive property to multiply x-4 by 2x+3 and combine like terms.

$$2x^{2}+2.5x-2=2x^{2}-5x-12-5$$

Subtract 5 from -12 to get -17.

$$2x^{2}+2.5x-2=2x^{2}-5x-17$$

Subtract 2x^{2} from both sides.

$$2x^{2}+2.5x-2-2x^{2}=-5x-17$$

Combine 2x^{2} and -2x^{2} to get 0.

$$2.5x-2=-5x-17$$

Add 5x to both sides.

$$2.5x-2+5x=-17$$

Combine 2.5x and 5x to get 7.5x.

$$7.5x-2=-17$$

Add 2 to both sides.

$$7.5x=-17+2$$

Add -17 and 2 to get -15.

$$7.5x=-15$$

Divide both sides by 7.5.

$$x=\frac{-15}{7.5}$$

Expand \frac{-15}{7.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{-150}{75}$$

Divide -150 by 75 to get -2.

$$x=-2$$