Questions: Solve for (u). (-u=3 u^2-2) (u=)

Transcript text: Solve for $u$. \[ -u=3 u^{2}-2 \] \[ u= \]

Solution

Step 1: Rearranging the Equation

We start with the equation: \[ -u = 3u^2 - 2 \] Rearranging this gives us: \[ 3u^2 + u - 2 = 0 \]

Step 2: Factoring the Polynomial

Next, we factor the polynomial $3u^2 + u - 2$. The factorization results in: \[ (3u - 2)(u + 1) = 0 \]

Step 3: Finding the Solutions

To find the values of $u$, we set each factor equal to zero:

Step 4: Listing the Solutions

The solutions for $u$ are: \[ u = -1, \frac{2}{3} \]

$ u = -1, \frac{2}{3} $

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