Solve for y (complex solution)
\left\{\begin{matrix}y=0\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&x=\frac{3}{2}\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=\frac{3}{2}=1.5\text{, }&\text{unconditionally}\\x\neq 0\text{, }&y=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=0\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&x=\frac{3}{2}\end{matrix}\right.
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y=\frac{3y}{2x}
Express \frac{3}{2x}y as a single fraction.
y-\frac{3y}{2x}=0
Subtract \frac{3y}{2x} from both sides.
\frac{y\times 2x}{2x}-\frac{3y}{2x}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{2x}{2x}.
\frac{y\times 2x-3y}{2x}=0
Since \frac{y\times 2x}{2x} and \frac{3y}{2x} have the same denominator, subtract them by subtracting their numerators.
y\times 2x-3y=0
Multiply both sides of the equation by 2x.
\left(2x-3\right)y=0
Combine all terms containing y.
y=0
Divide 0 by 2x-3.
y\times 2x=3y
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x.
2xy=3y
Reorder the terms.
2yx=3y
The equation is in standard form.
\frac{2yx}{2y}=\frac{3y}{2y}
Divide both sides by 2y.
x=\frac{3y}{2y}
Dividing by 2y undoes the multiplication by 2y.
x=\frac{3}{2}
Divide 3y by 2y.
y=\frac{3y}{2x}
Express \frac{3}{2x}y as a single fraction.
y-\frac{3y}{2x}=0
Subtract \frac{3y}{2x} from both sides.
\frac{y\times 2x}{2x}-\frac{3y}{2x}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{2x}{2x}.
\frac{y\times 2x-3y}{2x}=0
Since \frac{y\times 2x}{2x} and \frac{3y}{2x} have the same denominator, subtract them by subtracting their numerators.
y\times 2x-3y=0
Multiply both sides of the equation by 2x.
\left(2x-3\right)y=0
Combine all terms containing y.
y=0
Divide 0 by 2x-3.
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}