Solve the equation by factoring.  `6x^2 + 6 = -13x`

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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the first step to solving this equation would be to add the -13x to both sides to we can move to the other side where the other terms are located:

`6x^2 + 6 +13x = -13x + 13x`

`6x^2 + 6 +13x = 0`
I rearranged the terms in descending order to make it easier on me:

`6x^2 + 13x + 6`

Now:

Try seeing this problem as `ax^2 + bx + c`

Because there is a 6 in front the "a", we must multiply a by c

 

`6 xx 6 =36 `

Find factors of 36 that add up to b aka 13

these numbers will be 9 and 4, now plug them in as b

`6x^2 + 9x + 4x + 6`

now group:

`(6x^2 + 9x) +( 4x + 6)`

no you factor the parentheses:

`3x (2x + 3) + 2 (2x+3)`

`(3x+2) ( 2x + 3)`

set the parentheses equal to 0

3x + 2 =0

3x = -2

x =` -2/3` or .66

2x + 3 = 0

2x = -3

x = `-3/2` or -1.5

to check:

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