Solve (2x+3)(x-4)=2(x^2-6)-5x

$$( 2 x + 3 ) ( x - 4 ) = 2 ( x ^ { 2 } - 6 ) - 5 x$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

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

$$2x^{2}-5x-12=2\left(x^{2}-6\right)-5x$$

Use the distributive property to multiply 2 by x^{2}-6.

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

Subtract 2x^{2} from both sides.

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

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

$$-5x-12=-12-5x$$

Subtract -12 from both sides.

$$-5x-12-\left(-12\right)=-5x$$

The opposite of -12 is 12.

$$-5x-12+12=-5x$$

Add 5x to both sides.

$$-5x-12+12+5x=0$$

Add -12 and 12 to get 0.

$$-5x+5x=0$$

Combine -5x and 5x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

$$2x^{2}-5x-12=2\left(x^{2}-6\right)-5x$$

Use the distributive property to multiply 2 by x^{2}-6.

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

Subtract 2x^{2} from both sides.

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

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

$$-5x-12=-12-5x$$

Subtract -12 from both sides.

$$-5x-12-\left(-12\right)=-5x$$

The opposite of -12 is 12.

$$-5x-12+12=-5x$$

Add 5x to both sides.

$$-5x-12+12+5x=0$$

Add -12 and 12 to get 0.

$$-5x+5x=0$$

Combine -5x and 5x to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$