Solve -11x^2-2(2m-3)x+2m+5=0(1)

$$- 11 x ^ { 2 } - 2 ( 2 m - 3 ) x + 2 m + 5 = 0 ( 1 )$$

Solve for m

$$m=-\frac{\left(1-x\right)\left(11x+5\right)}{2\left(1-2x\right)}$$

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Multiply 0 and 1 to get 0.

$$-11x^{2}-2\left(2m-3\right)x+2m+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-11x^{2}-2\left(2m-3\right)x+2m=-5$$

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

$$-11x^{2}+\left(-4m+6\right)x+2m=-5$$

Use the distributive property to multiply -4m+6 by x.

$$-11x^{2}-4mx+6x+2m=-5$$

Add 11x^{2} to both sides.

$$-4mx+6x+2m=-5+11x^{2}$$

Subtract 6x from both sides.

$$-4mx+2m=-5+11x^{2}-6x$$

Combine all terms containing m.

$$\left(-4x+2\right)m=-5+11x^{2}-6x$$

The equation is in standard form.

$$\left(2-4x\right)m=11x^{2}-6x-5$$

Divide both sides by -4x+2.

$$\frac{\left(2-4x\right)m}{2-4x}=\frac{\left(x-1\right)\left(11x+5\right)}{2-4x}$$

Dividing by -4x+2 undoes the multiplication by -4x+2.

$$m=\frac{\left(x-1\right)\left(11x+5\right)}{2-4x}$$

Divide \left(-1+x\right)\left(5+11x\right) by -4x+2.

$$m=\frac{\left(x-1\right)\left(11x+5\right)}{2\left(1-2x\right)}$$

Solve for x

$$x=\frac{-\sqrt{4m^{2}+10m+64}-2m+3}{11}$$

$$x=\frac{\sqrt{4m^{2}+10m+64}-2m+3}{11}$$