4×2-12x+9=0

Rewrite 4×2 as (2x)2.

(2x)2-12x+9=0

Rewrite 9 as 32.

(2x)2-12x+32=0

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

2ab=2⋅(2x)⋅-3

Simplify.

2ab=-12x

Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=2x and b=-3.

(2x-3)2=0

(2x-3)2=0

Set the 2x-3 equal to 0.

2x-3=0

Add 3 to both sides of the equation.

2x=3

Divide each term by 2 and simplify.

Divide each term in 2x=3 by 2.

2×2=32

Cancel the common factor of 2.

Cancel the common factor.

2×2=32

Divide x by 1.

x=32

x=32

x=32

x=32

Solve using the Square Root Property 4x^2-12x+9=0