Solve the following equation by factoring. $$ 6\left(p^{2}-1 ight)=5 p $$ Rewrite the equation in a completely factored form. $$ \begin{array}{l}(3 p+2)(2 p-3)=0 \ ext { (Type your answer in factored form.) } \ ext { The solution set is }\{\square\} \ ext { (Simplify your answer. Type an integer or a simplified fraction. Use a comma to separate answers as needed.) }\end{array} $$

Question

Solve the following equation by factoring. $$ 6\left(p^{2}-1ight)=5 p $$ Rewrite the equation in a completely factored form. $$ \begin{array}{l}(3 p+2)(2 p-3)=0 \ 	ext { (Type your answer in factored form.) } \ 	ext { The solution set is }\{\square\} \ 	ext { (Simplify your answer. Type an integer or a simplified fraction. Use a comma to separate answers as needed.) }\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation $$ 6(p^{2}-1)=5p $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$6\left(p^{2}-1\right)=5p$$
- step1: Expand the expression:
  $$6p^{2}-6=5p$$
- step2: Move the expression to the left side:
  $$6p^{2}-6-5p=0$$
- step3: Factor the expression:
  $$\left(2p-3\right)\left(3p+2\right)=0$$
- step4: Separate into possible cases:
  $$\begin{align}&2p-3=0\&3p+2=0\end{align}$$
- step5: Solve the equation:
  $$\begin{align}&p=\frac{3}{2}\&p=-\frac{2}{3}\end{align}$$
- step6: Rewrite:
  $$p_{1}=-\frac{2}{3},p_{2}=\frac{3}{2}$$
The solutions to the equation $$6(p^{2}-1)=5p$$ are $$p=-\frac{2}{3}$$ and $$p=\frac{3}{2}$$.

Now, let's rewrite the equation in a completely factored form:
$$6(p^{2}-1)=5p$$

Factoring the equation:
$$(3p+2)(2p-3)=0$$

Therefore, the solution set is $$\left\{-\frac{2}{3}, \frac{3}{2}\right\}$$.
The solutions are $$ p = -\frac{2}{3} $$ and $$ p = \frac{3}{2} $$.

Solve the following equation by factoring.

Rewrite the equation in a completely factored form.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions

Solve the following equation by factoring. Rewrite the equation in a completely factored form.