# Let a=x^2+4. How do you rewrite (x^2+4)^2 +32 = 12x^2+48 in terms of a and set it equal to zero.?

Feb 22, 2017

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

#### Explanation:

${\left({x}^{2} + 4\right)}^{2} + 32 = 12 {x}^{2} + 48$ is equivalent to (factorizing RHS)

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

But as $a = {x}^{2} + 4$, this can be written as

${a}^{2} + 32 = 12 \times a$

or ${a}^{2} + 32 = 12 a$

or ${a}^{2} - 12 a + 32 = 0$