Questions: Solve for v. -12v-9=4v^2

Transcript text: Solve for $v$. \[ -12 v-9=4 v^{2} \]

Solution

Solution Steps

Step 1: Rearranging the Equation

We start with the equation: \[ -12v - 9 = 4v^{2} \] Rearranging it to standard polynomial form gives: \[ 4v^{2} + 12v + 9 = 0 \]

Step 2: Factoring the Polynomial

Next, we factor the polynomial $4v^{2} + 12v + 9$. The factorization results in: \[ (2v + 3)^{2} = 0 \]

Step 3: Solving for $v$

To find the solutions for $v$, we set the factored expression equal to zero: \[ (2v + 3)^{2} = 0 \] Taking the square root of both sides, we have: \[ 2v + 3 = 0 \] Solving for $v$ gives: \[ v = -\frac{3}{2} \]

Final Answer

$\boxed{v = -\frac{3}{2}}$

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