The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
-4((x-1)-1)((x-1)+1)=0
Remove the parentheses around the expression x-1.
-4(x-1-1)((x-1)+1)=0
Subtract 1 from -1 to get -2.
-4(x-2)((x-1)+1)=0
Remove the parentheses around the expression x-1.
-4(x-2)(x-1+1)=0
Add 1 to -1 to get 0.
-4(x-2)(x)=0
Remove the parentheses.
-4*x(x-2)=0
Multiply -4 by x to get -4x.
(-4x)(x-2)=0
Remove the parentheses.
-4x(x-2)=0
If any individual factor on the left-hand side of the equation is equal to 0, the entire expression will be equal to 0.
-4x=0_(x-2)=0
Set the first factor equal to 0 and solve.
-4x=0
Divide each term in the equation by -4.
-(4x)/(-4)=(0)/(-4)
Simplify the left-hand side of the equation by canceling the common terms.
x=(0)/(-4)
Any expression with zero in the numerator is zero.
x=0
Set the next factor equal to 0 and solve.
(x-2)=0
Remove the parentheses around the expression x-2.
x-2=0
Since -2 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2 to both sides.
x=2
The final solution is all the values that make -4x(x-2)=0 true. The multiplicity of a root is the number of times the root appears. For example, a factor of has multiplicity of .
x=0,2