Question

How do you solve `6h^2+17h+12=0`?

Answer 1

`6h^2 + 17h +12 = 0`

We can Split the Middle Term of this equation to factorise it and then find the solution for the equation

In this technique, if we have to factorise an expression like `ah^2 + bh + c`, we need to think of 2 numbers such that:
`N_1 xx N_2 = a xx c = 6 xx 12 = 72`
and
`N_1 +N_2 = b = 17`

After trying out a few numbers we get `N_1 = 9` and `N_2 =8`
`9 xx 8 = 72`, and `9 +8 = 17`

`6h^2 + 17h +12 = 6h^2 + 9h +8h +12`
`= 3h (2h + 3) + 4(2h + 3)`
`= (3h +4) (2h + 3)`
the solution for the equation is :
`color(blue)h=-4/3`
`color(blue)h= -3/2`

Answer 2

The answer is `h=-3/2, -4/3`

Problem: Solve `6h^2+17h+12=0` .

Multiply `6` times `12` to get `72`.
Find two numbers that when multiplied equal `72` and when added equal `17`.
Numbers `8` and `9` meet the criteria.
Write the equation substituting `8h` and `9h` for `17h`.

`6h^2+8h+9h+12=0`

Separate the first two terms from the second two terms.

`(6h^2+8h)+(9h+12)`

Factor out the GCF from both sets of terms.

`2h(3h+4)+3(3h+4)=0`

Factor out the GCF `(3h+4)` .

`(3h+4)(2h+3)=0`

Solve for `h`.

`3h+4=0`

`3h=-4`

`h=-4/3`

`2h+3=0`

`2h=-3`

`h=-3/2`

`h=-3/2, -4/3`