# how do you solve 3x^4 + 11x^3=4x^2

## To solve the equation 3x^4 + 11x^3 = 4x^2, you can follow these steps:

Step 1: Rearrange the equation to have zero on one side:

3x^4 + 11x^3 - 4x^2 = 0

Step 2: Factor the equation:

x^2(3x^2 + 11x - 4) = 0

Step 3: Solve for x using the Zero Product Property:

x^2 = 0 or 3x^2 + 11x - 4 = 0

Step 4: Solve the first equation:

x^2 = 0

x = 0 (since the square of zero is zero)

Step 5: Solve the quadratic equation:

3x^2 + 11x - 4 = 0

You can use the quadratic formula to find the solutions of this equation:

x = (-b +/- √(b^2 - 4ac)) / (2a)

For this equation, a = 3, b = 11, and c = -4. Substituting these values, we have:

x = (-(11) +/- √((11)^2 - 4(3)(-4))) / (2(3))

x = (-11 +/- √(121 + 48)) / 6

x = (-11 +/- √169) / 6

x = (-11 +/- 13) / 6

This gives us two potential solutions:

x = (-11 + 13) / 6 = 2 / 6 = 1/3

x = (-11 - 13) / 6 = -24 / 6 = -4

Therefore, the solutions to the equation 3x^4 + 11x^3 = 4x^2 are x = 0, x = 1/3, and x = -4.