solve for M 2(3m+2)^2+7(3m+2)=-6?

start by multiplying out:

2(9m^2 + 12m + 4) + 21m + 14 = -6

18m^2 + 24m + 8 + 21m + 14 = -6

then collect terms:

18m^2 + 45m + 28 = 0

then solve the quadratic using the quadratic theorem,

(-b +/- sqrt(b^2 - 4ac))/2a, where the quadratic is of the form am^2 + bm + c , which yeilds the answers:

m = -4/3 & -7/6

Let x = 3m + 2
2x² + 7x + 6 = 0
x = [ - 7 ± √(49-48) ] / 4
x = [ - 7 ± √(1) ] / 4
x = - 3 / 2 , x = - 2
3m + 2 = - 3/2 , 3m + 2 = - 2
3m = - 7/2 , 3m = - 4
m = - 7/6 , m = - 4/3

while working with inequalities, manage the inequality sign as you may and equivalent sign different than, while multiplying or dividing the two sides via a destructive quantity, opposite the inequality sign. 4x + 6 ? 2 4x ? 2 - 6 4x ? - 4 x ? - 4 / 4 x ? - a million 3x - 22 ? - 13 3x ? - 13 + 22 3x ? 9 x ? 9 / 3 x ? 3 ((- a million ? x ? ?) U (3 ? x ? ?) ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ To graph, build a dotted line from - a million to 3 with a closed circle on - a million and 3, then build a sturdy line from 3 to ? with a sturdy circle on 3.  

2(9m^2+12m+4)+7(3m+2)+6=0
18·m^2 + 45m + 28 =0

m= [-45±√9]/36 --> m= - 4/3 and m=-7/6

Saludos

2(9m^2+12m+4)+21m+14=-6
18m^2+24m+8+21m+14=-6
18m^2+45m+22=-6
18m^2+45m=-28
6m^2+45m+28=0

D=45^2-4*6*28=2025-672=1353>0

m1=(-45+36,78)/12 and
m2=(-45-36,78 )/12

as i alsways like to say about such quesions "break it down"
solve it in smaller groups before solving the whole
so 7(3m+2) = (21m + 14)

and 2(3m+2)^2 = 2[ (3m+2)(3m+2) ]
= 2[ 9m²+6m +6m+4 ]
= [ 18m²+24m +8 ]
now put all together to give
: [ 18m²+24m +8 ] + (21m + 14) = -6
18m² +24m+21m +8+14 = -6
18m² + 45m + 22 = -6
from the above stage you can group all to one side to give
: 18m² + 45m + 28 = 0
and then 'complete the squares' to find the value of m
18m² + 21m + 16m + 28 = 0
factorize to give (3m+4)(6m+7)=0

3m+4=0 6m+7=0
3m=-4 6m=-7
m=-4/3 m=-6/7

Substitute X for (3m+2)

2X²+7X=-6
2X²+7X+6=0
(2X+3)(X+2)=0

2X+3=0
2X=-3
X=-3/2

X+2=0
X=-2

Substitute 3M+2 for X and solve to find the answer(s)!!!

2(3m+2)^2+7(3m+2)=-6
2(9m^2+12m+4)+21m+14=-6
18m^2+24m+8+21m+14+6=0
18m^2+45m+28=0
(3m+4)(6m+7)=0

3m+4=0
3m=-4
m=-4/3

6m+7=0
6m=-7
m=-6/7