# Solve for x 8x^4+8x^3+8x^2+8x=0 8×4+8×3+8×2+8x=0
Factor the left side of the equation.
Factor 8x out of 8×4+8×3+8×2+8x.
Factor 8x out of 8×4.
8x(x3)+8×3+8×2+8x=0
Factor 8x out of 8×3.
8x(x3)+8x(x2)+8×2+8x=0
Factor 8x out of 8×2.
8x(x3)+8x(x2)+8x(x)+8x=0
Factor 8x out of 8x.
8x(x3)+8x(x2)+8x(x)+8x(1)=0
Factor 8x out of 8x(x3)+8x(x2).
8x(x3+x2)+8x(x)+8x(1)=0
Factor 8x out of 8x(x3+x2)+8x(x).
8x(x3+x2+x)+8x(1)=0
Factor 8x out of 8x(x3+x2+x)+8x(1).
8x(x3+x2+x+1)=0
8x(x3+x2+x+1)=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
8x((x3+x2)+x+1)=0
Factor out the greatest common factor (GCF) from each group.
8x(x2(x+1)+1(x+1))=0
8x(x2(x+1)+1(x+1))=0
Factor.
Factor the polynomial by factoring out the greatest common factor, x+1.
8x((x+1)(x2+1))=0
Remove unnecessary parentheses.
8x(x+1)(x2+1)=0
8x(x+1)(x2+1)=0
8x(x+1)(x2+1)=0
Divide each term by 8 and simplify.
Divide each term in 8x(x+1)(x2+1)=0 by 8.
8x(x+1)(x2+1)8=08
Simplify 8x(x+1)(x2+1)8.
Simplify terms.
Cancel the common factor of 8.
Cancel the common factor.
8x(x+1)(x2+1)8=08
Divide (x(x+1))(x2+1) by 1.
(x(x+1))(x2+1)=08
(x(x+1))(x2+1)=08
Apply the distributive property.
(x⋅x+x⋅1)(x2+1)=08
Simplify the expression.
Multiply x by x.
(x2+x⋅1)(x2+1)=08
Multiply x by 1.
(x2+x)(x2+1)=08
(x2+x)(x2+1)=08
(x2+x)(x2+1)=08
Expand (x2+x)(x2+1) using the FOIL Method.
Apply the distributive property.
x2(x2+1)+x(x2+1)=08
Apply the distributive property.
x2x2+x2⋅1+x(x2+1)=08
Apply the distributive property.
x2x2+x2⋅1+x⋅x2+x⋅1=08
x2x2+x2⋅1+x⋅x2+x⋅1=08
Simplify each term.
Multiply x2 by x2 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
x2+2+x2⋅1+x⋅x2+x⋅1=08
Add 2 and 2.
x4+x2⋅1+x⋅x2+x⋅1=08
x4+x2⋅1+x⋅x2+x⋅1=08
Multiply x2 by 1.
x4+x2+x⋅x2+x⋅1=08
Multiply x by x2 by adding the exponents.
Multiply x by x2.
Raise x to the power of 1.
x4+x2+x1x2+x⋅1=08
Use the power rule aman=am+n to combine exponents.
x4+x2+x1+2+x⋅1=08
x4+x2+x1+2+x⋅1=08
Add 1 and 2.
x4+x2+x3+x⋅1=08
x4+x2+x3+x⋅1=08
Multiply x by 1.
x4+x2+x3+x=08
x4+x2+x3+x=08
x4+x2+x3+x=08
Divide 0 by 8.
x4+x2+x3+x=0
x4+x2+x3+x=0
Factor the left side of the equation.
Factor x out of x4+x2+x3+x.
Factor x out of x4.
x⋅x3+x2+x3+x=0
Factor x out of x2.
x⋅x3+x⋅x+x3+x=0
Factor x out of x3.
x⋅x3+x⋅x+x⋅x2+x=0
Raise x to the power of 1.
x⋅x3+x⋅x+x⋅x2+x=0
Factor x out of x1.
x⋅x3+x⋅x+x⋅x2+x⋅1=0
Factor x out of x⋅x3+x⋅x.
x(x3+x)+x⋅x2+x⋅1=0
Factor x out of x(x3+x)+x⋅x2.
x(x3+x+x2)+x⋅1=0
Factor x out of x(x3+x+x2)+x⋅1.
x(x3+x+x2+1)=0
x(x3+x+x2+1)=0
Reorder terms.
x(x3+x2+x+1)=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
x((x3+x2)+x+1)=0
Factor out the greatest common factor (GCF) from each group.
x(x2(x+1)+1(x+1))=0
x(x2(x+1)+1(x+1))=0
Factor.
Factor the polynomial by factoring out the greatest common factor, x+1.
x((x+1)(x2+1))=0
Remove unnecessary parentheses.
x(x+1)(x2+1)=0
x(x+1)(x2+1)=0
x(x+1)(x2+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.
x=0
x+1=0
x2+1=0
Set the first factor equal to 0.
x=0
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x+1=0
Subtract 1 from both sides of the equation.
x=-1
x=-1
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x2+1=0
Subtract 1 from both sides of the equation.
x2=-1
Take the square root of both sides of the equation to eliminate the exponent on the left side.
x=±-1
The complete solution is the result of both the positive and negative portions of the solution.
Rewrite -1 as i.
x=±i
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
x=i
Next, use the negative value of the ± to find the second solution.
x=-i
The complete solution is the result of both the positive and negative portions of the solution.
x=i,-i
x=i,-i
x=i,-i
x=i,-i
The final solution is all the values that make x(x+1)(x2+1)=0 true.
x=0,-1,i,-i
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