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t\left(3-2t\right)
Factor out t.
-2t^{2}+3t=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.
t=\frac{-3±\sqrt{3^{2}}}{2\left(-2\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.
t=\frac{-3±3}{2\left(-2\right)}
Take the square root of 3^{2}.
t=\frac{-3±3}{-4}
Multiply 2 times -2.
t=\frac{0}{-4}
Now solve the equation t=\frac{-3±3}{-4} when ± is plus. Add -3 to 3.
t=0
Divide 0 by -4.
t=-\frac{6}{-4}
Now solve the equation t=\frac{-3±3}{-4} when ± is minus. Subtract 3 from -3.
t=\frac{3}{2}
Reduce the fraction \frac{-6}{-4} to lowest terms by extracting and canceling out 2.
-2t^{2}+3t=-2t\left(t-\frac{3}{2}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and \frac{3}{2} for x_{2}.
-2t^{2}+3t=-2t\times \frac{-2t+3}{-2}
Subtract \frac{3}{2} from t by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
-2t^{2}+3t=t\left(-2t+3\right)
Cancel out 2, the greatest common factor in -2 and -2.