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

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

Solve for k

$$k=-3-\frac{1}{4x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply 4 and -3 to get -12.

$$-1-4kx^{2}-12x^{2}=0$$

Add 12x^{2} to both sides. Anything plus zero gives itself.

$$-1-4kx^{2}=12x^{2}$$

Add 1 to both sides.

$$-4kx^{2}=12x^{2}+1$$

The equation is in standard form.

$$\left(-4x^{2}\right)k=12x^{2}+1$$

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

$$\frac{\left(-4x^{2}\right)k}{-4x^{2}}=\frac{12x^{2}+1}{-4x^{2}}$$

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

$$k=\frac{12x^{2}+1}{-4x^{2}}$$

Divide 12x^{2}+1 by -4x^{2}.

$$k=-3-\frac{1}{4x^{2}}$$

Solve for x (complex solution)

$$x=-\frac{i\left(k+3\right)^{-\frac{1}{2}}}{2}$$

$$x=\frac{i\left(k+3\right)^{-\frac{1}{2}}}{2}\text{, }k\neq -3$$

Solve for x

$$x=\frac{\sqrt{-\frac{1}{k+3}}}{2}$$

$$x=-\frac{\sqrt{-\frac{1}{k+3}}}{2}\text{, }k<-3$$