Solve 6*10^-9/r^2+4*10^-9/0*25-r+r^2=0

$$\frac{ 6 \times { 10 }^{ -9 } }{ { r }^{ 2 } } + \frac{ 4 \times { 10 }^{ -9 } }{ 0 \cdot 25-r+ { r }^{ 2 } } = 0$$

Solve for r

$$r=\frac{3}{5}=0.6$$

Steps for Solving Linear Equation

Variable r cannot be equal to any of the values 0,1 since division by zero is not defined. Multiply both sides of the equation by \left(r-1\right)r^{2}, the least common multiple of r^{2},0\times 25-r+r^{2}.

$$\left(r-1\right)\times 6\times 10^{-9}+r\times 4\times 10^{-9}=0$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\left(r-1\right)\times 6\times \frac{1}{1000000000}+r\times 4\times 10^{-9}=0$$

Multiply 6 and \frac{1}{1000000000} to get \frac{3}{500000000}.

$$\left(r-1\right)\times \frac{3}{500000000}+r\times 4\times 10^{-9}=0$$

Use the distributive property to multiply r-1 by \frac{3}{500000000}.

$$\frac{3}{500000000}r-\frac{3}{500000000}+r\times 4\times 10^{-9}=0$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{3}{500000000}r-\frac{3}{500000000}+r\times 4\times \frac{1}{1000000000}=0$$

Multiply 4 and \frac{1}{1000000000} to get \frac{1}{250000000}.

$$\frac{3}{500000000}r-\frac{3}{500000000}+r\times \frac{1}{250000000}=0$$

Combine \frac{3}{500000000}r and r\times \frac{1}{250000000} to get \frac{1}{100000000}r.

$$\frac{1}{100000000}r-\frac{3}{500000000}=0$$

Add \frac{3}{500000000} to both sides. Anything plus zero gives itself.

$$\frac{1}{100000000}r=\frac{3}{500000000}$$

Multiply both sides by 100000000, the reciprocal of \frac{1}{100000000}.

$$r=\frac{3}{500000000}\times 100000000$$

Multiply \frac{3}{500000000} and 100000000 to get \frac{3}{5}.

$$r=\frac{3}{5}$$