w4-w=0

Factor w out of w4-w.

Factor w out of w4.

w⋅w3-w=0

Factor w out of -w.

w⋅w3+w⋅-1=0

Factor w out of w⋅w3+w⋅-1.

w(w3-1)=0

w(w3-1)=0

Rewrite 1 as 13.

w(w3-13)=0

Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=w and b=1.

w((w-1)(w2+w⋅1+12))=0

Factor.

Simplify.

Multiply w by 1.

w((w-1)(w2+w+12))=0

One to any power is one.

w((w-1)(w2+w+1))=0

w((w-1)(w2+w+1))=0

Remove unnecessary parentheses.

w(w-1)(w2+w+1)=0

w(w-1)(w2+w+1)=0

w(w-1)(w2+w+1)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

w=0

w-1=0

w2+w+1=0

Set the first factor equal to 0.

w=0

Set the next factor equal to 0.

w-1=0

Add 1 to both sides of the equation.

w=1

w=1

Set the next factor equal to 0.

w2+w+1=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=1, and c=1 into the quadratic formula and solve for w.

-1±12-4⋅(1⋅1)2⋅1

Simplify.

Simplify the numerator.

One to any power is one.

w=-1±1-4⋅(1⋅1)2⋅1

Multiply 1 by 1.

w=-1±1-4⋅12⋅1

Multiply -4 by 1.

w=-1±1-42⋅1

Subtract 4 from 1.

w=-1±-32⋅1

Rewrite -3 as -1(3).

w=-1±-1⋅32⋅1

Rewrite -1(3) as -1⋅3.

w=-1±-1⋅32⋅1

Rewrite -1 as i.

w=-1±i32⋅1

w=-1±i32⋅1

Multiply 2 by 1.

w=-1±i32

w=-1±i32

The final answer is the combination of both solutions.

w=-1-i32,-1+i32

w=-1-i32,-1+i32

The final solution is all the values that make w(w-1)(w2+w+1)=0 true.

w=0,1,-1-i32,-1+i32

Solve for w w^4-w=0