Solve $\color{blue}{-x^2+4x-4 = 0}$ using factoring.
First we need to factor trinomial $ \color{blue}{ -x^2+4x-4 } $ and than we use factored form to solve an equation $ \color{blue}{ -x^2+4x-4 = 0} $.
Step 1: We can simplify equation by multiplying both sides by -1. After multiplying we have the following equation:
$$ \begin{aligned} -x^2+4x-4 &= 0 \,\,\, / \color{orangered}{\cdot \, -1 } \\[0.9 em ] x^2-4x+4 &=0 \end{aligned} $$Step 2:
Both the first and third terms are perfect squares.
$$ x^2 = \left( \color{blue}{ x } \right)^2 ~~ \text{and} ~~ 4 = \left( \color{red}{ 2 } \right)^2 $$The middle term ( $ -4x $ ) is two times the product of the terms that are squared.
$$ -4x = - 2 \cdot \color{blue}{x} \cdot \color{red}{2} $$We can conclude that the polynomial $ x^{2}-4x+4 $ is a perfect square trinomial, so we will use the formula below.
$$ A^2 - 2AB + B^2 = (A - B)^2 $$In this example we have $ \color{blue}{ A = x } $ and $ \color{red}{ B = 2 } $ so,
$$ x^{2}-4x+4 = ( \color{blue}{ x } - \color{red}{ 2 } )^2 $$Step 3: Set each factor to zero and solve equations.
$$ \begin{array}{ccc} \begin{aligned} x-2 &= 0 \\ x &= 2 \end{aligned} & ~ & \begin{aligned} x-2 &= 0 \\ x &= 2 \end{aligned} \end{array} $$