Solve for x 32+x^2=12x

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

Subtract $12 x$ from both sides of the equation.

$32 + x^{2} - 12 x = 0$

Factor $32 + x^{2} - 12 x$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $32$ and whose sum is $- 12$ .

$- 8, - 4$

Write the factored form using these integers.

$(x - 8) (x - 4) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 8 = 0$

$x - 4 = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $(x - 8) (x - 4) = 0$ true.

$x = 8, 4$

Solve for x 32+x^2=12x

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