Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{y}{x}+4\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{y}{4-b}\text{, }&b\neq 4\\x\in \mathrm{C}\text{, }&y=0\text{ and }b=4\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{y}{x}+4\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{y}{4-b}\text{, }&b\neq 4\\x\in \mathrm{R}\text{, }&y=0\text{ and }b=4\end{matrix}\right.
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14x+3y=2x+3bx
Use the distributive property to multiply 2+3b by x.
2x+3bx=14x+3y
Swap sides so that all variable terms are on the left hand side.
3bx=14x+3y-2x
Subtract 2x from both sides.
3bx=12x+3y
Combine 14x and -2x to get 12x.
3xb=12x+3y
The equation is in standard form.
\frac{3xb}{3x}=\frac{12x+3y}{3x}
Divide both sides by 3x.
b=\frac{12x+3y}{3x}
Dividing by 3x undoes the multiplication by 3x.
b=\frac{y}{x}+4
Divide 12x+3y by 3x.
14x+3y=2x+3bx
Use the distributive property to multiply 2+3b by x.
14x+3y-2x=3bx
Subtract 2x from both sides.
12x+3y=3bx
Combine 14x and -2x to get 12x.
12x+3y-3bx=0
Subtract 3bx from both sides.
12x-3bx=-3y
Subtract 3y from both sides. Anything subtracted from zero gives its negation.
\left(12-3b\right)x=-3y
Combine all terms containing x.
\frac{\left(12-3b\right)x}{12-3b}=-\frac{3y}{12-3b}
Divide both sides by -3b+12.
x=-\frac{3y}{12-3b}
Dividing by -3b+12 undoes the multiplication by -3b+12.
x=-\frac{y}{4-b}
Divide -3y by -3b+12.
14x+3y=2x+3bx
Use the distributive property to multiply 2+3b by x.
2x+3bx=14x+3y
Swap sides so that all variable terms are on the left hand side.
3bx=14x+3y-2x
Subtract 2x from both sides.
3bx=12x+3y
Combine 14x and -2x to get 12x.
3xb=12x+3y
The equation is in standard form.
\frac{3xb}{3x}=\frac{12x+3y}{3x}
Divide both sides by 3x.
b=\frac{12x+3y}{3x}
Dividing by 3x undoes the multiplication by 3x.
b=\frac{y}{x}+4
Divide 12x+3y by 3x.
14x+3y=2x+3bx
Use the distributive property to multiply 2+3b by x.
14x+3y-2x=3bx
Subtract 2x from both sides.
12x+3y=3bx
Combine 14x and -2x to get 12x.
12x+3y-3bx=0
Subtract 3bx from both sides.
12x-3bx=-3y
Subtract 3y from both sides. Anything subtracted from zero gives its negation.
\left(12-3b\right)x=-3y
Combine all terms containing x.
\frac{\left(12-3b\right)x}{12-3b}=-\frac{3y}{12-3b}
Divide both sides by -3b+12.
x=-\frac{3y}{12-3b}
Dividing by -3b+12 undoes the multiplication by -3b+12.
x=-\frac{y}{4-b}
Divide -3y by -3b+12.
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}