Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&x_{3}=-\frac{x_{6}}{6}+\frac{1}{10}\end{matrix}\right.
Solve for x_3 (complex solution)
\left\{\begin{matrix}\\x_{3}=-\frac{x_{6}}{6}+\frac{1}{10}\text{, }&\text{unconditionally}\\x_{3}\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&x_{3}=-\frac{x_{6}}{6}+\frac{1}{10}\end{matrix}\right.
Solve for x_3
\left\{\begin{matrix}\\x_{3}=-\frac{x_{6}}{6}+\frac{1}{10}\text{, }&\text{unconditionally}\\x_{3}\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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3x-30x_{3}x=5x_{6}x
Multiply 5 and 6 to get 30.
3x-30x_{3}x-5x_{6}x=0
Subtract 5x_{6}x from both sides.
\left(3-30x_{3}-5x_{6}\right)x=0
Combine all terms containing x.
\left(3-5x_{6}-30x_{3}\right)x=0
The equation is in standard form.
x=0
Divide 0 by 3-30x_{3}-5x_{6}.
3x-30x_{3}x=5x_{6}x
Multiply 5 and 6 to get 30.
-30x_{3}x=5x_{6}x-3x
Subtract 3x from both sides.
\left(-30x\right)x_{3}=5xx_{6}-3x
The equation is in standard form.
\frac{\left(-30x\right)x_{3}}{-30x}=\frac{x\left(5x_{6}-3\right)}{-30x}
Divide both sides by -30x.
x_{3}=\frac{x\left(5x_{6}-3\right)}{-30x}
Dividing by -30x undoes the multiplication by -30x.
x_{3}=-\frac{x_{6}}{6}+\frac{1}{10}
Divide x\left(-3+5x_{6}\right) by -30x.
3x-30x_{3}x=5x_{6}x
Multiply 5 and 6 to get 30.
3x-30x_{3}x-5x_{6}x=0
Subtract 5x_{6}x from both sides.
\left(3-30x_{3}-5x_{6}\right)x=0
Combine all terms containing x.
\left(3-5x_{6}-30x_{3}\right)x=0
The equation is in standard form.
x=0
Divide 0 by 3-30x_{3}-5x_{6}.
3x-30x_{3}x=5x_{6}x
Multiply 5 and 6 to get 30.
-30x_{3}x=5x_{6}x-3x
Subtract 3x from both sides.
\left(-30x\right)x_{3}=5xx_{6}-3x
The equation is in standard form.
\frac{\left(-30x\right)x_{3}}{-30x}=\frac{x\left(5x_{6}-3\right)}{-30x}
Divide both sides by -30x.
x_{3}=\frac{x\left(5x_{6}-3\right)}{-30x}
Dividing by -30x undoes the multiplication by -30x.
x_{3}=-\frac{x_{6}}{6}+\frac{1}{10}
Divide x\left(-3+5x_{6}\right) by -30x.
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}