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3x^{2}-5x+3+8x-4
Combine 6x^{2} and -3x^{2} to get 3x^{2}.
3x^{2}+3x+3-4
Combine -5x and 8x to get 3x.
3x^{2}+3x-1
Subtract 4 from 3 to get -1.
factor(3x^{2}-5x+3+8x-4)
Combine 6x^{2} and -3x^{2} to get 3x^{2}.
factor(3x^{2}+3x+3-4)
Combine -5x and 8x to get 3x.
factor(3x^{2}+3x-1)
Subtract 4 from 3 to get -1.
3x^{2}+3x-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{-3±\sqrt{3^{2}-4\times 3\left(-1\right)}}{2\times 3}
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{-3±\sqrt{9-4\times 3\left(-1\right)}}{2\times 3}
Square 3.
x=\frac{-3±\sqrt{9-12\left(-1\right)}}{2\times 3}
Multiply -4 times 3.
x=\frac{-3±\sqrt{9+12}}{2\times 3}
Multiply -12 times -1.
x=\frac{-3±\sqrt{21}}{2\times 3}
Add 9 to 12.
x=\frac{-3±\sqrt{21}}{6}
Multiply 2 times 3.
x=\frac{\sqrt{21}-3}{6}
Now solve the equation x=\frac{-3±\sqrt{21}}{6} when ± is plus. Add -3 to \sqrt{21}.
x=\frac{\sqrt{21}}{6}-\frac{1}{2}
Divide -3+\sqrt{21} by 6.
x=\frac{-\sqrt{21}-3}{6}
Now solve the equation x=\frac{-3±\sqrt{21}}{6} when ± is minus. Subtract \sqrt{21} from -3.
x=-\frac{\sqrt{21}}{6}-\frac{1}{2}
Divide -3-\sqrt{21} by 6.
3x^{2}+3x-1=3\left(x-\left(\frac{\sqrt{21}}{6}-\frac{1}{2}\right)\right)\left(x-\left(-\frac{\sqrt{21}}{6}-\frac{1}{2}\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\frac{1}{2}+\frac{\sqrt{21}}{6} for x_{1} and -\frac{1}{2}-\frac{\sqrt{21}}{6} for x_{2}.