Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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\left(0\times 43+1x-140\right)\times 0\times 57=0\times 5x
Multiply 40 and 0 to get 0.
\left(0+1x-140\right)\times 0\times 57=0\times 5x
Multiply 0 and 43 to get 0.
\left(-140+1x\right)\times 0\times 57=0\times 5x
Subtract 140 from 0 to get -140.
\left(-140+1x\right)\times 0=0\times 5x
Multiply 0 and 57 to get 0.
0=0\times 5x
Anything times zero gives zero.
0=0x
Multiply 0 and 5 to get 0.
0=0
Anything times zero gives zero.
\text{true}
Compare 0 and 0.
x\in \mathrm{C}
This is true for any x.
\left(0\times 43+1x-140\right)\times 0\times 57=0\times 5x
Multiply 40 and 0 to get 0.
\left(0+1x-140\right)\times 0\times 57=0\times 5x
Multiply 0 and 43 to get 0.
\left(-140+1x\right)\times 0\times 57=0\times 5x
Subtract 140 from 0 to get -140.
\left(-140+1x\right)\times 0=0\times 5x
Multiply 0 and 57 to get 0.
0=0\times 5x
Anything times zero gives zero.
0=0x
Multiply 0 and 5 to get 0.
0=0
Anything times zero gives zero.
\text{true}
Compare 0 and 0.
x\in \mathrm{R}
This is true for any x.
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}