Solve for x
x\in \mathrm{R}
Solve for z
z\in \mathrm{R}
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3x^{2}z-9x^{2}z^{2}=3x^{2}z-9x^{2}z^{2}
Use the distributive property to multiply 3x^{2}z by 1-3z.
3x^{2}z-9x^{2}z^{2}-3x^{2}z=-9x^{2}z^{2}
Subtract 3x^{2}z from both sides.
3x^{2}z-9x^{2}z^{2}-3x^{2}z+9x^{2}z^{2}=0
Add 9x^{2}z^{2} to both sides.
-9x^{2}z^{2}+9x^{2}z^{2}=0
Combine 3x^{2}z and -3x^{2}z to get 0.
0=0
Combine -9x^{2}z^{2} and 9x^{2}z^{2} to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{R}
This is true for any x.
3x^{2}z-9x^{2}z^{2}=3x^{2}z-9x^{2}z^{2}
Use the distributive property to multiply 3x^{2}z by 1-3z.
3x^{2}z-9x^{2}z^{2}-3x^{2}z=-9x^{2}z^{2}
Subtract 3x^{2}z from both sides.
3x^{2}z-9x^{2}z^{2}-3x^{2}z+9x^{2}z^{2}=0
Add 9x^{2}z^{2} to both sides.
-9x^{2}z^{2}+9x^{2}z^{2}=0
Combine 3x^{2}z and -3x^{2}z to get 0.
0=0
Combine -9x^{2}z^{2} and 9x^{2}z^{2} to get 0.
\text{true}
Compare 0 and 0.
z\in \mathrm{R}
This is true for any z.
Examples
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{ 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}