3×2-36x+108=0

Factor 3 out of 3×2-36x+108.

Factor 3 out of 3×2.

3(x2)-36x+108=0

Factor 3 out of -36x.

3(x2)+3(-12x)+108=0

Factor 3 out of 108.

3×2+3(-12x)+3⋅36=0

Factor 3 out of 3×2+3(-12x).

3(x2-12x)+3⋅36=0

Factor 3 out of 3(x2-12x)+3⋅36.

3(x2-12x+36)=0

3(x2-12x+36)=0

Factor using the perfect square rule.

Rewrite 36 as 62.

3(x2-12x+62)=0

Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.

2ab=2⋅x⋅-6

Simplify.

2ab=-12x

Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=x and b=-6.

3(x-6)2=0

3(x-6)2=0

3(x-6)2=0

Divide each term in 3(x-6)2=0 by 3.

3(x-6)23=03

Cancel the common factor of 3.

Cancel the common factor.

3(x-6)23=03

Divide (x-6)2 by 1.

(x-6)2=03

(x-6)2=03

Divide 0 by 3.

(x-6)2=0

(x-6)2=0

Set the x-6 equal to 0.

x-6=0

Add 6 to both sides of the equation.

x=6

Solve using the Square Root Property 3x^2-36x+108=0