Solve x^2-2(1+3m)x+7(3+2m)=0

$$x ^ { 2 } - 2 ( 1 + 3 m ) x + 7 ( 3 + 2 m ) = 0$$

Solve for m

$$m=-\frac{x^{2}-2x+21}{2\left(7-3x\right)}$$

$$x\neq \frac{7}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 3+2m.

$$x^{2}-2\left(1+3m\right)x+21+14m=0$$

Subtract 21 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-2\left(1+3m\right)x+14m=-21$$

Use the distributive property to multiply -2 by 1+3m.

$$x^{2}+\left(-2-6m\right)x+14m=-21$$

Use the distributive property to multiply -2-6m by x.

$$x^{2}-2x-6mx+14m=-21$$

Subtract x^{2} from both sides.

$$-2x-6mx+14m=-21-x^{2}$$

Add 2x to both sides.

$$-6mx+14m=-21-x^{2}+2x$$

Combine all terms containing m.

$$\left(-6x+14\right)m=-21-x^{2}+2x$$

The equation is in standard form.

$$\left(14-6x\right)m=-x^{2}+2x-21$$

Divide both sides by -6x+14.

$$\frac{\left(14-6x\right)m}{14-6x}=\frac{-x^{2}+2x-21}{14-6x}$$

Dividing by -6x+14 undoes the multiplication by -6x+14.

$$m=\frac{-x^{2}+2x-21}{14-6x}$$

Divide -21-x^{2}+2x by -6x+14.

$$m=\frac{-x^{2}+2x-21}{2\left(7-3x\right)}$$

Solve for x (complex solution)

$$x=\sqrt{\left(m-2\right)\left(9m+10\right)}+3m+1$$

$$x=-\sqrt{\left(m-2\right)\left(9m+10\right)}+3m+1$$

Solve for x

$$x=\sqrt{\left(m-2\right)\left(9m+10\right)}+3m+1$$

$$x=-\sqrt{\left(m-2\right)\left(9m+10\right)}+3m+1\text{, }m\leq -\frac{10}{9}\text{ or }m\geq 2$$