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2\left(3x^{2}-4x\right)
Factor out 2.
x\left(3x-4\right)
Consider 3x^{2}-4x. Factor out x.
2x\left(3x-4\right)
Rewrite the complete factored expression.
6x^{2}-8x=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{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2\times 6}
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{-\left(-8\right)±8}{2\times 6}
Take the square root of \left(-8\right)^{2}.
x=\frac{8±8}{2\times 6}
The opposite of -8 is 8.
x=\frac{8±8}{12}
Multiply 2 times 6.
x=\frac{16}{12}
Now solve the equation x=\frac{8±8}{12} when ± is plus. Add 8 to 8.
x=\frac{4}{3}
Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.
x=\frac{0}{12}
Now solve the equation x=\frac{8±8}{12} when ± is minus. Subtract 8 from 8.
x=0
Divide 0 by 12.
6x^{2}-8x=6\left(x-\frac{4}{3}\right)x
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{4}{3} for x_{1} and 0 for x_{2}.
6x^{2}-8x=6\times \frac{3x-4}{3}x
Subtract \frac{4}{3} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
6x^{2}-8x=2\left(3x-4\right)x
Cancel out 3, the greatest common factor in 6 and 3.