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Solve for x (complex solution)
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3+4x+x\left(x+1\right)\left(-1\right)=\left(x+1\right)\times 3-xx
Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+1\right), the least common multiple of x^{2}+x,x,x+1.
3+4x+x\left(x+1\right)\left(-1\right)=\left(x+1\right)\times 3-x^{2}
Multiply x and x to get x^{2}.
3+4x+\left(x^{2}+x\right)\left(-1\right)=\left(x+1\right)\times 3-x^{2}
Use the distributive property to multiply x by x+1.
3+4x-x^{2}-x=\left(x+1\right)\times 3-x^{2}
Use the distributive property to multiply x^{2}+x by -1.
3+3x-x^{2}=\left(x+1\right)\times 3-x^{2}
Combine 4x and -x to get 3x.
3+3x-x^{2}=3x+3-x^{2}
Use the distributive property to multiply x+1 by 3.
3+3x-x^{2}-3x=3-x^{2}
Subtract 3x from both sides.
3-x^{2}=3-x^{2}
Combine 3x and -3x to get 0.
3-x^{2}-3=-x^{2}
Subtract 3 from both sides.
-x^{2}=-x^{2}
Subtract 3 from 3 to get 0.
-x^{2}+x^{2}=0
Add x^{2} to both sides.
0=0
Combine -x^{2} and x^{2} to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{C}
This is true for any x.
x\in \mathrm{C}\setminus -1,0
Variable x cannot be equal to any of the values -1,0.
3+4x+x\left(x+1\right)\left(-1\right)=\left(x+1\right)\times 3-xx
Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+1\right), the least common multiple of x^{2}+x,x,x+1.
3+4x+x\left(x+1\right)\left(-1\right)=\left(x+1\right)\times 3-x^{2}
Multiply x and x to get x^{2}.
3+4x+\left(x^{2}+x\right)\left(-1\right)=\left(x+1\right)\times 3-x^{2}
Use the distributive property to multiply x by x+1.
3+4x-x^{2}-x=\left(x+1\right)\times 3-x^{2}
Use the distributive property to multiply x^{2}+x by -1.
3+3x-x^{2}=\left(x+1\right)\times 3-x^{2}
Combine 4x and -x to get 3x.
3+3x-x^{2}=3x+3-x^{2}
Use the distributive property to multiply x+1 by 3.
3+3x-x^{2}-3x=3-x^{2}
Subtract 3x from both sides.
3-x^{2}=3-x^{2}
Combine 3x and -3x to get 0.
3-x^{2}-3=-x^{2}
Subtract 3 from both sides.
-x^{2}=-x^{2}
Subtract 3 from 3 to get 0.
-x^{2}+x^{2}=0
Add x^{2} to both sides.
0=0
Combine -x^{2} and x^{2} to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{R}
This is true for any x.
x\in \mathrm{R}\setminus -1,0
Variable x cannot be equal to any of the values -1,0.