# Chapter 6 - Section 6.6 - Solving Quadratic Equations by Factoring - Exercise Set: 57

The solutions are 0 and 4 and 8.

#### Work Step by Step

$x^{3}$-12$x^{2}$+32x=0 x($x^{2}$-12$x^{}$+32)=0 x($x^{2}$-4$x^{}$-8x+32)=0 x[x(x-4)-8(x-4)]=0 x(x-8)(x-4)=0 x=0 or x-8=0 or x-4=0 x=0 or x=8 or x=4 The solutions are 0 and 4 and 8. Check Let x=0 $x^{3}$-12$x^{2}$+32x=0 $0^{3}$-12$0^{2}$+32*0=0 0-0+0=0 0=0 Let x=4 $x^{3}$-12$x^{2}$+32x=0 $4^{3}$-12$4^{2}$+32*4=0 64-12*16+128=0 64-192+128=0 0=0 Let x=8 $x^{3}$-12$x^{2}$+32x=0 $8^{3}$-12$8^{2}$+32*8=0 512-12*64+256=0 512-768+256=0 768-768=0 0=0

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