Solve for m (complex solution)
\left\{\begin{matrix}m=\frac{-7x^{2}-15x+A-4}{2\left(3x+5\right)}\text{, }&x\neq -\frac{5}{3}\\m\in \mathrm{C}\text{, }&A=-\frac{14}{9}\text{ and }x=-\frac{5}{3}\end{matrix}\right.
Solve for A
A=7x^{2}+6mx+15x+10m+4
Solve for m
\left\{\begin{matrix}m=\frac{-7x^{2}-15x+A-4}{2\left(3x+5\right)}\text{, }&x\neq -\frac{5}{3}\\m\in \mathrm{R}\text{, }&A=-\frac{14}{9}\text{ and }x=-\frac{5}{3}\end{matrix}\right.
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A=9x^{2}+6mx+12x+m^{2}+4m+4-\left(x-m\right)^{2}-\left(x+2m\right)\left(x-3\right)
Square 3x+m+2.
A=9x^{2}+6mx+12x+m^{2}+4m+4-\left(x^{2}-2xm+m^{2}\right)-\left(x+2m\right)\left(x-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-m\right)^{2}.
A=9x^{2}+6mx+12x+m^{2}+4m+4-x^{2}+2xm-m^{2}-\left(x+2m\right)\left(x-3\right)
To find the opposite of x^{2}-2xm+m^{2}, find the opposite of each term.
A=8x^{2}+6mx+12x+m^{2}+4m+4+2xm-m^{2}-\left(x+2m\right)\left(x-3\right)
Combine 9x^{2} and -x^{2} to get 8x^{2}.
A=8x^{2}+8mx+12x+m^{2}+4m+4-m^{2}-\left(x+2m\right)\left(x-3\right)
Combine 6mx and 2xm to get 8mx.
A=8x^{2}+8mx+12x+4m+4-\left(x+2m\right)\left(x-3\right)
Combine m^{2} and -m^{2} to get 0.
A=8x^{2}+8mx+12x+4m+4-\left(x^{2}-3x+2mx-6m\right)
Use the distributive property to multiply x+2m by x-3.
A=8x^{2}+8mx+12x+4m+4-x^{2}+3x-2mx+6m
To find the opposite of x^{2}-3x+2mx-6m, find the opposite of each term.
A=7x^{2}+8mx+12x+4m+4+3x-2mx+6m
Combine 8x^{2} and -x^{2} to get 7x^{2}.
A=7x^{2}+8mx+15x+4m+4-2mx+6m
Combine 12x and 3x to get 15x.
A=7x^{2}+6mx+15x+4m+4+6m
Combine 8mx and -2mx to get 6mx.
A=7x^{2}+6mx+15x+10m+4
Combine 4m and 6m to get 10m.
7x^{2}+6mx+15x+10m+4=A
Swap sides so that all variable terms are on the left hand side.
6mx+15x+10m+4=A-7x^{2}
Subtract 7x^{2} from both sides.
6mx+10m+4=A-7x^{2}-15x
Subtract 15x from both sides.
6mx+10m=A-7x^{2}-15x-4
Subtract 4 from both sides.
\left(6x+10\right)m=A-7x^{2}-15x-4
Combine all terms containing m.
\left(6x+10\right)m=-7x^{2}-15x+A-4
The equation is in standard form.
\frac{\left(6x+10\right)m}{6x+10}=\frac{-7x^{2}-15x+A-4}{6x+10}
Divide both sides by 6x+10.
m=\frac{-7x^{2}-15x+A-4}{6x+10}
Dividing by 6x+10 undoes the multiplication by 6x+10.
m=\frac{-7x^{2}-15x+A-4}{2\left(3x+5\right)}
Divide A-7x^{2}-15x-4 by 6x+10.
A=9x^{2}+6mx+12x+m^{2}+4m+4-\left(x-m\right)^{2}-\left(x+2m\right)\left(x-3\right)
Square 3x+m+2.
A=9x^{2}+6mx+12x+m^{2}+4m+4-\left(x^{2}-2xm+m^{2}\right)-\left(x+2m\right)\left(x-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-m\right)^{2}.
A=9x^{2}+6mx+12x+m^{2}+4m+4-x^{2}+2xm-m^{2}-\left(x+2m\right)\left(x-3\right)
To find the opposite of x^{2}-2xm+m^{2}, find the opposite of each term.
A=8x^{2}+6mx+12x+m^{2}+4m+4+2xm-m^{2}-\left(x+2m\right)\left(x-3\right)
Combine 9x^{2} and -x^{2} to get 8x^{2}.
A=8x^{2}+8mx+12x+m^{2}+4m+4-m^{2}-\left(x+2m\right)\left(x-3\right)
Combine 6mx and 2xm to get 8mx.
A=8x^{2}+8mx+12x+4m+4-\left(x+2m\right)\left(x-3\right)
Combine m^{2} and -m^{2} to get 0.
A=8x^{2}+8mx+12x+4m+4-\left(x^{2}-3x+2mx-6m\right)
Use the distributive property to multiply x+2m by x-3.
A=8x^{2}+8mx+12x+4m+4-x^{2}+3x-2mx+6m
To find the opposite of x^{2}-3x+2mx-6m, find the opposite of each term.
A=7x^{2}+8mx+12x+4m+4+3x-2mx+6m
Combine 8x^{2} and -x^{2} to get 7x^{2}.
A=7x^{2}+8mx+15x+4m+4-2mx+6m
Combine 12x and 3x to get 15x.
A=7x^{2}+6mx+15x+4m+4+6m
Combine 8mx and -2mx to get 6mx.
A=7x^{2}+6mx+15x+10m+4
Combine 4m and 6m to get 10m.
A=9x^{2}+6mx+12x+m^{2}+4m+4-\left(x-m\right)^{2}-\left(x+2m\right)\left(x-3\right)
Square 3x+m+2.
A=9x^{2}+6mx+12x+m^{2}+4m+4-\left(x^{2}-2xm+m^{2}\right)-\left(x+2m\right)\left(x-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-m\right)^{2}.
A=9x^{2}+6mx+12x+m^{2}+4m+4-x^{2}+2xm-m^{2}-\left(x+2m\right)\left(x-3\right)
To find the opposite of x^{2}-2xm+m^{2}, find the opposite of each term.
A=8x^{2}+6mx+12x+m^{2}+4m+4+2xm-m^{2}-\left(x+2m\right)\left(x-3\right)
Combine 9x^{2} and -x^{2} to get 8x^{2}.
A=8x^{2}+8mx+12x+m^{2}+4m+4-m^{2}-\left(x+2m\right)\left(x-3\right)
Combine 6mx and 2xm to get 8mx.
A=8x^{2}+8mx+12x+4m+4-\left(x+2m\right)\left(x-3\right)
Combine m^{2} and -m^{2} to get 0.
A=8x^{2}+8mx+12x+4m+4-\left(x^{2}-3x+2mx-6m\right)
Use the distributive property to multiply x+2m by x-3.
A=8x^{2}+8mx+12x+4m+4-x^{2}+3x-2mx+6m
To find the opposite of x^{2}-3x+2mx-6m, find the opposite of each term.
A=7x^{2}+8mx+12x+4m+4+3x-2mx+6m
Combine 8x^{2} and -x^{2} to get 7x^{2}.
A=7x^{2}+8mx+15x+4m+4-2mx+6m
Combine 12x and 3x to get 15x.
A=7x^{2}+6mx+15x+4m+4+6m
Combine 8mx and -2mx to get 6mx.
A=7x^{2}+6mx+15x+10m+4
Combine 4m and 6m to get 10m.
7x^{2}+6mx+15x+10m+4=A
Swap sides so that all variable terms are on the left hand side.
6mx+15x+10m+4=A-7x^{2}
Subtract 7x^{2} from both sides.
6mx+10m+4=A-7x^{2}-15x
Subtract 15x from both sides.
6mx+10m=A-7x^{2}-15x-4
Subtract 4 from both sides.
\left(6x+10\right)m=A-7x^{2}-15x-4
Combine all terms containing m.
\left(6x+10\right)m=-7x^{2}-15x+A-4
The equation is in standard form.
\frac{\left(6x+10\right)m}{6x+10}=\frac{-7x^{2}-15x+A-4}{6x+10}
Divide both sides by 6x+10.
m=\frac{-7x^{2}-15x+A-4}{6x+10}
Dividing by 6x+10 undoes the multiplication by 6x+10.
m=\frac{-7x^{2}-15x+A-4}{2\left(3x+5\right)}
Divide A-7x^{2}-15x-4 by 6x+10.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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
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