Question

Solve:

$3c^2=10c-8$

Short answer

The solutions of the quadratic equations $3c^2=10c-8$are $c=\frac{4}{3},2$

Step-by-step solution

Step 1. Given Information

An equation:

$3c^2=10c-8$

Step 2. Write the quadratic equation in standard form.

$$\begin{gathered} 3c^2=10c-8 \\ 3c^2-10c+8=0 \end{gathered}$$

Step 3. Factor the quadratic expression

Factorize the equation,

$$\begin{gathered} 3c^2-10c+8=0 \\ (3c-4)(c-2)=0 \end{gathered}$$

Step 4. Use the Zero-Product property

Use the Zero Product Property and set each factor to zero.

$$\begin{gathered} (3c-4)(c-2)=0 \\ 3c-4=0 \\ c=\frac{4}{3} \\ c-2=0 \\ c=2 \end{gathered}$$

The value of c is $c=\frac{4}{3},2$

Step 5. Check the answer

Check by substituting the values in the original equation,

When $c=\frac{4}{3}$,

$$\begin{gathered} 3{\left(\frac{4}{3}\right)}^2=10\left(\frac{4}{3}\right)-8 \\ \frac{16}{3}=\frac{40}{3}-8 \\ \frac{16-40}{3}=8 \\ -8=-8 \end{gathered}$$

When $c=2$,

$$\begin{gathered} 3{\left(2\right)}^2=10\left(2\right)-8 \\ 12=20-8 \\ 12=12 \end{gathered}$$

Hence the equations hold true.