Question

Solve by factoring6h^2+8h+2=0

Answer 1

h=-1/3, -1

Explanation:

Given the equation:

`6h^2+8h+2=0`

To solve the equation by factoring, follow the steps below:

Step 1: Multiply the coefficient of h² and the constant.

`6*2=12`

Step 2: Find two numbers that multiply to give 12, and add to give the coefficient of h, 8.

• To do this, list the ,factors of the product,, 12: 1,2,3,4,6, and 12.

• Then select your two numbers by observation.

`\begin{gathered} 6h+2h=8h \\ (6h)(2h)=12h^2 \end{gathered}`

Step 3: Rewrite the middle with those numbers.

`6h^2+6h+2h+2=0`

Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.

`\begin{gathered} 6h(h+1)+2(h+1)=0 \\ (6h+2)(h+1)=0 \end{gathered}`

Step 5: Solve for h.

`\begin{gathered} 6h+2=0\text{ or }h+1=0 \\ 6h=-2\text{ or }h=-1 \\ h=-(2)/(6),h=-1 \\ h=-(1)/(3),h=-1 \end{gathered}`

The solutions to the equation are -1/3 and -1.