Solve 3x^2-mxleft(x+4right)=4xleft(x-1right)+8x

$$3 { x }^{ 2 } -mx \left( x+4 \right) = 4x \left( x-1 \right) +8x$$

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=-1\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&x=-4\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply mx by x+4.

$$3x^{2}-\left(mx^{2}+4mx\right)=4x\left(x-1\right)+8x$$

To find the opposite of mx^{2}+4mx, find the opposite of each term.

$$3x^{2}-mx^{2}-4mx=4x\left(x-1\right)+8x$$

Use the distributive property to multiply 4x by x-1.

$$3x^{2}-mx^{2}-4mx=4x^{2}-4x+8x$$

Combine -4x and 8x to get 4x.

$$3x^{2}-mx^{2}-4mx=4x^{2}+4x$$

Subtract 3x^{2} from both sides.

$$-mx^{2}-4mx=4x^{2}+4x-3x^{2}$$

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$-mx^{2}-4mx=x^{2}+4x$$

Combine all terms containing m.

$$\left(-x^{2}-4x\right)m=x^{2}+4x$$

Divide both sides by -x^{2}-4x.

$$\frac{\left(-x^{2}-4x\right)m}{-x^{2}-4x}=\frac{x\left(x+4\right)}{-x^{2}-4x}$$

Dividing by -x^{2}-4x undoes the multiplication by -x^{2}-4x.

$$m=\frac{x\left(x+4\right)}{-x^{2}-4x}$$

Divide x\left(4+x\right) by -x^{2}-4x.

$$m=-1$$

Solve for m

$$\left\{\begin{matrix}\\m=-1\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&x=-4\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply mx by x+4.

$$3x^{2}-\left(mx^{2}+4mx\right)=4x\left(x-1\right)+8x$$

To find the opposite of mx^{2}+4mx, find the opposite of each term.

$$3x^{2}-mx^{2}-4mx=4x\left(x-1\right)+8x$$

Use the distributive property to multiply 4x by x-1.

$$3x^{2}-mx^{2}-4mx=4x^{2}-4x+8x$$

Combine -4x and 8x to get 4x.

$$3x^{2}-mx^{2}-4mx=4x^{2}+4x$$

Subtract 3x^{2} from both sides.

$$-mx^{2}-4mx=4x^{2}+4x-3x^{2}$$

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$-mx^{2}-4mx=x^{2}+4x$$

Combine all terms containing m.

$$\left(-x^{2}-4x\right)m=x^{2}+4x$$

Divide both sides by -x^{2}-4x.

$$\frac{\left(-x^{2}-4x\right)m}{-x^{2}-4x}=\frac{x\left(x+4\right)}{-x^{2}-4x}$$

Dividing by -x^{2}-4x undoes the multiplication by -x^{2}-4x.

$$m=\frac{x\left(x+4\right)}{-x^{2}-4x}$$

Divide x\left(4+x\right) by -x^{2}-4x.

$$m=-1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-4\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&m=-1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=-4\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&m=-1\end{matrix}\right.$$