Solve x^3-(4m-1)x^2-4(1-m)x+2=0

$$x ^ { 3 } - ( 4 m - 1 ) x ^ { 2 } - 4 ( 1 - m ) x + 2 = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{x}{4}+\frac{1}{2}-\frac{1}{2x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4m-1 by x^{2}.

$$x^{3}-\left(4mx^{2}-x^{2}\right)-4\left(1-m\right)x+2=0$$

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

$$x^{3}-4mx^{2}+x^{2}-4\left(1-m\right)x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

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

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

Use the distributive property to multiply -4+4m by x.

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

Subtract x^{3} from both sides.

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

Subtract x^{2} from both sides.

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

Add 4x to both sides.

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

Combine all terms containing m.

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

The equation is in standard form.

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

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

$$\frac{\left(4x-4x^{2}\right)m}{4x-4x^{2}}=\frac{\left(x-1\right)\left(2-2x-x^{2}\right)}{4x-4x^{2}}$$

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

$$m=\frac{\left(x-1\right)\left(2-2x-x^{2}\right)}{4x-4x^{2}}$$

Divide \left(-1+x\right)\left(2-2x-x^{2}\right) by -4x^{2}+4x.

$$m=\frac{x}{4}+\frac{1}{2}-\frac{1}{2x}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{x}{4}+\frac{1}{2}-\frac{1}{2x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4m-1 by x^{2}.

$$x^{3}-\left(4mx^{2}-x^{2}\right)-4\left(1-m\right)x+2=0$$

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

$$x^{3}-4mx^{2}+x^{2}-4\left(1-m\right)x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

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

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

Use the distributive property to multiply -4+4m by x.

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

Subtract x^{3} from both sides.

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

Subtract x^{2} from both sides.

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

Add 4x to both sides.

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

Combine all terms containing m.

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

The equation is in standard form.

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

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

$$\frac{\left(4x-4x^{2}\right)m}{4x-4x^{2}}=\frac{\left(x-1\right)\left(2-2x-x^{2}\right)}{4x-4x^{2}}$$

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

$$m=\frac{\left(x-1\right)\left(2-2x-x^{2}\right)}{4x-4x^{2}}$$

Divide \left(-1+x\right)\left(2-2x-x^{2}\right) by -4x^{2}+4x.

$$m=\frac{x}{4}+\frac{1}{2}-\frac{1}{2x}$$

Solve for x

$$x=\sqrt{4m^{2}-4m+3}+2m-1$$

$$x=-\sqrt{4m^{2}-4m+3}+2m-1$$

$$x=1$$