Solve for b
b=3y+n
x\neq 0
Solve for n
n=b-3y
x\neq 0
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y\times 3x=x\left(-n+b\right)
Multiply both sides of the equation by 3x.
y\times 3x=x\left(-n\right)+xb
Use the distributive property to multiply x by -n+b.
x\left(-n\right)+xb=y\times 3x
Swap sides so that all variable terms are on the left hand side.
xb=y\times 3x-x\left(-n\right)
Subtract x\left(-n\right) from both sides.
xb=y\times 3x+xn
Multiply -1 and -1 to get 1.
xb=nx+3xy
The equation is in standard form.
\frac{xb}{x}=\frac{x\left(3y+n\right)}{x}
Divide both sides by x.
b=\frac{x\left(3y+n\right)}{x}
Dividing by x undoes the multiplication by x.
b=3y+n
Divide x\left(3y+n\right) by x.
y\times 3x=x\left(-n+b\right)
Multiply both sides of the equation by 3x.
y\times 3x=x\left(-n\right)+xb
Use the distributive property to multiply x by -n+b.
x\left(-n\right)+xb=y\times 3x
Swap sides so that all variable terms are on the left hand side.
x\left(-n\right)=y\times 3x-xb
Subtract xb from both sides.
-nx=3xy-bx
Reorder the terms.
\left(-x\right)n=3xy-bx
The equation is in standard form.
\frac{\left(-x\right)n}{-x}=\frac{x\left(3y-b\right)}{-x}
Divide both sides by -x.
n=\frac{x\left(3y-b\right)}{-x}
Dividing by -x undoes the multiplication by -x.
n=b-3y
Divide x\left(3y-b\right) by -x.
Examples
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Linear equation
y = 3x + 4
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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}