Solve 2f(x)=3f(3x) 3f(3x-1)

Question

Solve the equation

Solve for x

Solve for f

x = 0 x = \frac{2 + 27 f}{81 f}

Evaluate

2 f x = 3 f \times 3 x \times 3 f (3 x - 1)

Multiply

More Steps

2 f x = 27 f^{2} x (3 x - 1)

Expand the expression

More Steps

2 f x = 81 f^{2} x^{2} - 27 f^{2} x

Move the expression to the left side

2 f x - (81 f^{2} x^{2} - 27 f^{2} x) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 f x - 81 f^{2} x^{2} + 27 f^{2} x = 0

Collect like terms by calculating the sum or difference of their coefficients

(2 f + 27 f^{2}) x - 81 f^{2} x^{2} = 0

Expand the expression

2 f x + 27 f^{2} x - 81 f^{2} x^{2} = 0

Factor the expression

More Steps

f x (2 + 27 f - 81 f x) = 0

When the product of factors equals 0,at least one factor is 0

f x = 0 2 + 27 f - 81 f x = 0

Solve the equation for x

x = 0 2 + 27 f - 81 f x = 0

Solution

More Steps

x = 0 x = \frac{2 + 27 f}{81 f}

Show Solution