Factor
6k\left(k-2\right)
Evaluate
6k\left(k-2\right)
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6\left(k^{2}-2k\right)
Factor out 6.
k\left(k-2\right)
Consider k^{2}-2k. Factor out k.
6k\left(k-2\right)
Rewrite the complete factored expression.
6k^{2}-12k=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.
k=\frac{-\left(-12\right)±\sqrt{\left(-12\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.
k=\frac{-\left(-12\right)±12}{2\times 6}
Take the square root of \left(-12\right)^{2}.
k=\frac{12±12}{2\times 6}
The opposite of -12 is 12.
k=\frac{12±12}{12}
Multiply 2 times 6.
k=\frac{24}{12}
Now solve the equation k=\frac{12±12}{12} when ± is plus. Add 12 to 12.
k=2
Divide 24 by 12.
k=\frac{0}{12}
Now solve the equation k=\frac{12±12}{12} when ± is minus. Subtract 12 from 12.
k=0
Divide 0 by 12.
6k^{2}-12k=6\left(k-2\right)k
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 2 for x_{1} and 0 for x_{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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