Question

${\boxed {\LARGE{\mathfrak {Question:-}}}}$

solve it

$\sf x(x+5)(x+7)(x+12)+150=0$​

Answer 1

$\large \pmb{\sf{Question :}}$

$\sf : \leadsto x(x+5)(x+7)(x+12)+150=0$

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$\large \pmb{\sf{Final \: Solution :}}$

$\color{green} \boxed{\sf{ \purple \bigstar \: \color{blue}x = - 6 \pm \sqrt{6} }} \\ \color{green} \boxed{\sf{ \purple \bigstar \: \color{blue}x = - 6 \pm \sqrt{31} }}$

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$\large \pmb{\sf{Step-by-step \: Solution :}}$

Let y = x + 6,

$\sf:⇝ (y -6)(y-1) (y+6)(y+1) + 150 = 0$

$\sf:⇝ ( y² - 1) (y² - 36 ) + 150 = 0$

$\sf:⇝ (y²)² - 37 y² + 186 = 0$

$\sf:⇝ (y² - 6) (y² - 31) = 0$

$\sf:⇝ y² = 6 \: ; \: y² = 31$

$\sf:⇝ y = ± \sqrt {6} \: ; \: y= ± \sqrt {31}$

$\pink \bigstar \: \color{green} \boxed{\sf \color{maroon}{:⇝ x = -6± \sqrt {6}\: \: ; \: \:x = -6±\sqrt {31}}}$

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$\sf \color{azure}\fcolorbox{pink}{black}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: @Saanvigrover2007 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}$