Solve -x^2+12x-32=-1(x-4)(x-8)

$$- x ^ { 2 } + 12 x - 32 = - 1 ( x - 4 ) ( x - 8 )$$

Solve for x (complex solution)

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

Solution Steps

Use the distributive property to multiply -1 by x-4.

$$-x^{2}+12x-32=\left(-x+4\right)\left(x-8\right)$$

Use the distributive property to multiply -x+4 by x-8 and combine like terms.

$$-x^{2}+12x-32=-x^{2}+12x-32$$

Add x^{2} to both sides.

$$-x^{2}+12x-32+x^{2}=12x-32$$

Subtract 12x from both sides.

$$-x^{2}+12x-32+x^{2}-12x=-32$$

Combine 12x and -12x to get 0.

$$-x^{2}-32+x^{2}=-32$$

Add 32 to both sides.

$$-x^{2}-32+x^{2}+32=0$$

Add -32 and 32 to get 0.

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

Combine -x^{2} and x^{2} 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 -1 by x-4.

$$-x^{2}+12x-32=\left(-x+4\right)\left(x-8\right)$$

Use the distributive property to multiply -x+4 by x-8 and combine like terms.

$$-x^{2}+12x-32=-x^{2}+12x-32$$

Add x^{2} to both sides.

$$-x^{2}+12x-32+x^{2}=12x-32$$

Subtract 12x from both sides.

$$-x^{2}+12x-32+x^{2}-12x=-32$$

Combine 12x and -12x to get 0.

$$-x^{2}-32+x^{2}=-32$$

Add 32 to both sides.

$$-x^{2}-32+x^{2}+32=0$$

Add -32 and 32 to get 0.

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

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

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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