Solve f(2a)+2f(b)=5(5(a+b))

$$f ( 2 a ) + 2 f ( b ) = 5 ( 5 ( a + b ) )$$

Solve for a

$$\left\{\begin{matrix}\\a=-b\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&f=\frac{25}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 5 and 5 to get 25.

$$f\times 2a+2fb=25\left(a+b\right)$$

Use the distributive property to multiply 25 by a+b.

$$f\times 2a+2fb=25a+25b$$

Subtract 25a from both sides.

$$f\times 2a+2fb-25a=25b$$

Subtract 2fb from both sides.

$$f\times 2a-25a=25b-2fb$$

Combine all terms containing a.

$$\left(f\times 2-25\right)a=25b-2fb$$

The equation is in standard form.

$$\left(2f-25\right)a=25b-2bf$$

Divide both sides by -25+2f.

$$\frac{\left(2f-25\right)a}{2f-25}=\frac{b\left(25-2f\right)}{2f-25}$$

Dividing by -25+2f undoes the multiplication by -25+2f.

$$a=\frac{b\left(25-2f\right)}{2f-25}$$

Divide b\left(25-2f\right) by -25+2f.

$$a=-b$$

Solve for b

$$\left\{\begin{matrix}\\b=-a\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&f=\frac{25}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 5 and 5 to get 25.

$$f\times 2a+2fb=25\left(a+b\right)$$

Use the distributive property to multiply 25 by a+b.

$$f\times 2a+2fb=25a+25b$$

Subtract 25b from both sides.

$$f\times 2a+2fb-25b=25a$$

Subtract f\times 2a from both sides.

$$2fb-25b=25a-f\times 2a$$

Multiply -1 and 2 to get -2.

$$2fb-25b=25a-2fa$$

Combine all terms containing b.

$$\left(2f-25\right)b=25a-2fa$$

The equation is in standard form.

$$\left(2f-25\right)b=25a-2af$$

Divide both sides by -25+2f.

$$\frac{\left(2f-25\right)b}{2f-25}=\frac{a\left(25-2f\right)}{2f-25}$$

Dividing by -25+2f undoes the multiplication by -25+2f.

$$b=\frac{a\left(25-2f\right)}{2f-25}$$

Divide a\left(25-2f\right) by -25+2f.

$$b=-a$$