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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2x\left(x^{3}-1\right)+\left(5x^{2}-1\right)\left(x-3\right)+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Use the distributive property to multiply 2x by x^{3}-1.

$$2x^{4}-2x+\left(5x^{2}-1\right)\left(x-3\right)+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Use the distributive property to multiply 5x^{2}-1 by x-3.

$$2x^{4}-2x+5x^{3}-15x^{2}-x+3+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Combine -2x and -x to get -3x.

$$2x^{4}-3x+5x^{3}-15x^{2}+3+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Combine -15x^{2} and 12x^{2} to get -3x^{2}.

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

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

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

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

$$2x^{4}-3x+5x^{3}-3x^{2}+3=2x^{4}+5x^{3}-3x^{2}$$

Subtract 2x^{4} from both sides.

$$2x^{4}-3x+5x^{3}-3x^{2}+3-2x^{4}=5x^{3}-3x^{2}$$

Combine 2x^{4} and -2x^{4} to get 0.

$$-3x+5x^{3}-3x^{2}+3=5x^{3}-3x^{2}$$

Subtract 5x^{3} from both sides.

$$-3x+5x^{3}-3x^{2}+3-5x^{3}=-3x^{2}$$

Combine 5x^{3} and -5x^{3} to get 0.

$$-3x-3x^{2}+3=-3x^{2}$$

Add 3x^{2} to both sides.

$$-3x-3x^{2}+3+3x^{2}=0$$

Combine -3x^{2} and 3x^{2} to get 0.

$$-3x+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-3$$

Divide both sides by -3.

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

Divide -3 by -3 to get 1.

$$x=1$$