Solve for x (complex solution)
x=-i
x=i
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3\left(2x^{2}+1\right)=\left(1-x\right)\times 6x-3\left(3+2x\right)
Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-1\right)\left(x+1\right), the least common multiple of x^{2}-1,-3-3x,1-x^{2}.
6x^{2}+3=\left(1-x\right)\times 6x-3\left(3+2x\right)
Use the distributive property to multiply 3 by 2x^{2}+1.
6x^{2}+3=\left(6-6x\right)x-3\left(3+2x\right)
Use the distributive property to multiply 1-x by 6.
6x^{2}+3=6x-6x^{2}-3\left(3+2x\right)
Use the distributive property to multiply 6-6x by x.
6x^{2}+3=6x-6x^{2}-9-6x
Use the distributive property to multiply -3 by 3+2x.
6x^{2}+3=-6x^{2}-9
Combine 6x and -6x to get 0.
6x^{2}+3+6x^{2}=-9
Add 6x^{2} to both sides.
12x^{2}+3=-9
Combine 6x^{2} and 6x^{2} to get 12x^{2}.
12x^{2}=-9-3
Subtract 3 from both sides.
12x^{2}=-12
Subtract 3 from -9 to get -12.
x^{2}=\frac{-12}{12}
Divide both sides by 12.
x^{2}=-1
Divide -12 by 12 to get -1.
x=i x=-i
The equation is now solved.
3\left(2x^{2}+1\right)=\left(1-x\right)\times 6x-3\left(3+2x\right)
Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-1\right)\left(x+1\right), the least common multiple of x^{2}-1,-3-3x,1-x^{2}.
6x^{2}+3=\left(1-x\right)\times 6x-3\left(3+2x\right)
Use the distributive property to multiply 3 by 2x^{2}+1.
6x^{2}+3=\left(6-6x\right)x-3\left(3+2x\right)
Use the distributive property to multiply 1-x by 6.
6x^{2}+3=6x-6x^{2}-3\left(3+2x\right)
Use the distributive property to multiply 6-6x by x.
6x^{2}+3=6x-6x^{2}-9-6x
Use the distributive property to multiply -3 by 3+2x.
6x^{2}+3=-6x^{2}-9
Combine 6x and -6x to get 0.
6x^{2}+3+6x^{2}=-9
Add 6x^{2} to both sides.
12x^{2}+3=-9
Combine 6x^{2} and 6x^{2} to get 12x^{2}.
12x^{2}+3+9=0
Add 9 to both sides.
12x^{2}+12=0
Add 3 and 9 to get 12.
x=\frac{0±\sqrt{0^{2}-4\times 12\times 12}}{2\times 12}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 12\times 12}}{2\times 12}
Square 0.
x=\frac{0±\sqrt{-48\times 12}}{2\times 12}
Multiply -4 times 12.
x=\frac{0±\sqrt{-576}}{2\times 12}
Multiply -48 times 12.
x=\frac{0±24i}{2\times 12}
Take the square root of -576.
x=\frac{0±24i}{24}
Multiply 2 times 12.
x=i
Now solve the equation x=\frac{0±24i}{24} when ± is plus.
x=-i
Now solve the equation x=\frac{0±24i}{24} when ± is minus.
x=i x=-i
The equation is now solved.
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Limits
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