Answer:
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=2,\:x=-3[/tex]
Step-by-step explanation:
Considering the equation
[tex]\left(4x\:-\:8\right)\left(3x\:+\:9\right)\:=\:0[/tex]
solving the equation
[tex]\left(4x\:-\:8\right)\left(3x\:+\:9\right)\:=\:0[/tex]
[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]\mathrm{Solve\:}\:4x-8=0[/tex]
[tex]4x-8=0[/tex]
[tex]4x-8+8=0+8[/tex]
[tex]4x=8[/tex]
[tex]x=2[/tex]
[tex]\mathrm{Solve\:}\:3x+9=0[/tex]
[tex]3x+9=0[/tex]
[tex]3x+9-9=0-9[/tex]
[tex]3x=-9[/tex]
[tex]x=-3[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=2,\:x=-3[/tex]
