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1-2\times 1\left(-3\right)x-3x^{2}
Calculate 1 to the power of 2 and get 1.
1-2\left(-3\right)x-3x^{2}
Multiply 2 and 1 to get 2.
1-\left(-6x\right)-3x^{2}
Multiply 2 and -3 to get -6.
1+6x-3x^{2}
The opposite of -6x is 6x.
factor(1-2\times 1\left(-3\right)x-3x^{2})
Calculate 1 to the power of 2 and get 1.
factor(1-2\left(-3\right)x-3x^{2})
Multiply 2 and 1 to get 2.
factor(1-\left(-6x\right)-3x^{2})
Multiply 2 and -3 to get -6.
factor(1+6x-3x^{2})
The opposite of -6x is 6x.
-3x^{2}+6x+1=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-6±\sqrt{6^{2}-4\left(-3\right)}}{2\left(-3\right)}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-6±\sqrt{36-4\left(-3\right)}}{2\left(-3\right)}
Square 6.
x=\frac{-6±\sqrt{36+12}}{2\left(-3\right)}
Multiply -4 times -3.
x=\frac{-6±\sqrt{48}}{2\left(-3\right)}
Add 36 to 12.
x=\frac{-6±4\sqrt{3}}{2\left(-3\right)}
Take the square root of 48.
x=\frac{-6±4\sqrt{3}}{-6}
Multiply 2 times -3.
x=\frac{4\sqrt{3}-6}{-6}
Now solve the equation x=\frac{-6±4\sqrt{3}}{-6} when ± is plus. Add -6 to 4\sqrt{3}.
x=-\frac{2\sqrt{3}}{3}+1
Divide -6+4\sqrt{3} by -6.
x=\frac{-4\sqrt{3}-6}{-6}
Now solve the equation x=\frac{-6±4\sqrt{3}}{-6} when ± is minus. Subtract 4\sqrt{3} from -6.
x=\frac{2\sqrt{3}}{3}+1
Divide -6-4\sqrt{3} by -6.
-3x^{2}+6x+1=-3\left(x-\left(-\frac{2\sqrt{3}}{3}+1\right)\right)\left(x-\left(\frac{2\sqrt{3}}{3}+1\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 1-\frac{2\sqrt{3}}{3} for x_{1} and 1+\frac{2\sqrt{3}}{3} for x_{2}.