Solve for E (complex solution)
\left\{\begin{matrix}E=-\frac{\left(3x+2\right)x^{2}}{n}\text{, }&n\neq 0\text{ and }x\neq 0\\E\in \mathrm{C}\text{, }&n=0\text{ and }x=-\frac{2}{3}\end{matrix}\right.
Solve for n (complex solution)
\left\{\begin{matrix}n=-\frac{\left(3x+2\right)x^{2}}{E}\text{, }&E\neq 0\text{ and }x\neq 0\\n\in \mathrm{C}\text{, }&E=0\text{ and }x=-\frac{2}{3}\end{matrix}\right.
Solve for E
\left\{\begin{matrix}E=-\frac{\left(3x+2\right)x^{2}}{n}\text{, }&n\neq 0\text{ and }x\neq 0\\E\in \mathrm{R}\text{, }&n=0\text{ and }x=-\frac{2}{3}\end{matrix}\right.
Solve for n
\left\{\begin{matrix}n=-\frac{\left(3x+2\right)x^{2}}{E}\text{, }&E\neq 0\text{ and }x\neq 0\\n\in \mathrm{R}\text{, }&E=0\text{ and }x=-\frac{2}{3}\end{matrix}\right.
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nE+3xx^{2}+x^{2}\times 2=0
Multiply both sides of the equation by x^{2}.
nE+3x^{3}+x^{2}\times 2=0
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
nE+x^{2}\times 2=-3x^{3}
Subtract 3x^{3} from both sides. Anything subtracted from zero gives its negation.
nE=-3x^{3}-x^{2}\times 2
Subtract x^{2}\times 2 from both sides.
nE=-3x^{3}-2x^{2}
Multiply -1 and 2 to get -2.
\frac{nE}{n}=-\frac{\left(3x+2\right)x^{2}}{n}
Divide both sides by n.
E=-\frac{\left(3x+2\right)x^{2}}{n}
Dividing by n undoes the multiplication by n.
nE+3xx^{2}+x^{2}\times 2=0
Multiply both sides of the equation by x^{2}.
nE+3x^{3}+x^{2}\times 2=0
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
nE+x^{2}\times 2=-3x^{3}
Subtract 3x^{3} from both sides. Anything subtracted from zero gives its negation.
nE=-3x^{3}-x^{2}\times 2
Subtract x^{2}\times 2 from both sides.
nE=-3x^{3}-2x^{2}
Multiply -1 and 2 to get -2.
En=-3x^{3}-2x^{2}
The equation is in standard form.
\frac{En}{E}=-\frac{\left(3x+2\right)x^{2}}{E}
Divide both sides by E.
n=-\frac{\left(3x+2\right)x^{2}}{E}
Dividing by E undoes the multiplication by E.
nE+3xx^{2}+x^{2}\times 2=0
Multiply both sides of the equation by x^{2}.
nE+3x^{3}+x^{2}\times 2=0
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
nE+x^{2}\times 2=-3x^{3}
Subtract 3x^{3} from both sides. Anything subtracted from zero gives its negation.
nE=-3x^{3}-x^{2}\times 2
Subtract x^{2}\times 2 from both sides.
nE=-3x^{3}-2x^{2}
Multiply -1 and 2 to get -2.
\frac{nE}{n}=-\frac{\left(3x+2\right)x^{2}}{n}
Divide both sides by n.
E=-\frac{\left(3x+2\right)x^{2}}{n}
Dividing by n undoes the multiplication by n.
nE+3xx^{2}+x^{2}\times 2=0
Multiply both sides of the equation by x^{2}.
nE+3x^{3}+x^{2}\times 2=0
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
nE+x^{2}\times 2=-3x^{3}
Subtract 3x^{3} from both sides. Anything subtracted from zero gives its negation.
nE=-3x^{3}-x^{2}\times 2
Subtract x^{2}\times 2 from both sides.
nE=-3x^{3}-2x^{2}
Multiply -1 and 2 to get -2.
En=-3x^{3}-2x^{2}
The equation is in standard form.
\frac{En}{E}=-\frac{\left(3x+2\right)x^{2}}{E}
Divide both sides by E.
n=-\frac{\left(3x+2\right)x^{2}}{E}
Dividing by E undoes the multiplication by E.
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}