Solve (5x+1)(2x-3)=(10x-9)(x+2)

$$( 5 x + 1 ) ( 2 x - 3 ) = ( 10 x - 9 ) ( x + 2 )$$

Solve for x

$$x=\frac{5}{8}=0.625$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5x+1 by 2x-3 and combine like terms.

$$10x^{2}-13x-3=\left(10x-9\right)\left(x+2\right)$$

Use the distributive property to multiply 10x-9 by x+2 and combine like terms.

$$10x^{2}-13x-3=10x^{2}+11x-18$$

Subtract 10x^{2} from both sides.

$$10x^{2}-13x-3-10x^{2}=11x-18$$

Combine 10x^{2} and -10x^{2} to get 0.

$$-13x-3=11x-18$$

Subtract 11x from both sides.

$$-13x-3-11x=-18$$

Combine -13x and -11x to get -24x.

$$-24x-3=-18$$

Add 3 to both sides.

$$-24x=-18+3$$

Add -18 and 3 to get -15.

$$-24x=-15$$

Divide both sides by -24.

$$x=\frac{-15}{-24}$$

Reduce the fraction \frac{-15}{-24} to lowest terms by extracting and canceling out -3.

$$x=\frac{5}{8}$$