Solve (2x+1)(x-5)=2(x^2-1)

$$( 2 x + 1 ) ( x - 5 ) = 2 ( x ^ { 2 } - 1 )$$

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

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

$$2x^{2}-9x-5=2\left(x^{2}-1\right)$$

Use the distributive property to multiply 2 by x^{2}-1.

$$2x^{2}-9x-5=2x^{2}-2$$

Subtract 2x^{2} from both sides.

$$2x^{2}-9x-5-2x^{2}=-2$$

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

$$-9x-5=-2$$

Add 5 to both sides.

$$-9x=-2+5$$

Add -2 and 5 to get 3.

$$-9x=3$$

Divide both sides by -9.

$$x=\frac{3}{-9}$$

Reduce the fraction \frac{3}{-9} to lowest terms by extracting and canceling out 3.

$$x=-\frac{1}{3}$$