Factor
6x\left(x-3\right)
Evaluate
6x\left(x-3\right)
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6\left(x^{2}-3x\right)
Factor out 6.
x\left(x-3\right)
Consider x^{2}-3x. Factor out x.
6x\left(x-3\right)
Rewrite the complete factored expression.
6x^{2}-18x=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(-18\right)±\sqrt{\left(-18\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(-18\right)±18}{2\times 6}
Take the square root of \left(-18\right)^{2}.
x=\frac{18±18}{2\times 6}
The opposite of -18 is 18.
x=\frac{18±18}{12}
Multiply 2 times 6.
x=\frac{36}{12}
Now solve the equation x=\frac{18±18}{12} when ± is plus. Add 18 to 18.
x=3
Divide 36 by 12.
x=\frac{0}{12}
Now solve the equation x=\frac{18±18}{12} when ± is minus. Subtract 18 from 18.
x=0
Divide 0 by 12.
6x^{2}-18x=6\left(x-3\right)x
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 3 for x_{1} and 0 for x_{2}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}