how do you sole this problem 7(b-6)=-12=b and11(2m+1)+12m=2+5(4=9m) also -(3-3p)+7(-2p-6)=-7p+9-10p-12making a note that i have analysis and...

While solving an equation, we add or subtract  equal quantity to both sides of an equation, with an intention of making the variable or unkowns to one side and the known or numbers to the other side. Similarly we can multiply or divide by equal quantity on both sides of an equation (except zero, which no number or no quantity!).

i)

Given:7(b-6)=-12-b or

7b-42=-12-b .

Add 42+b to both sides to make unknown bon left and numbers on right.

7b-42+42+b=-12-b+42-b and now simplify both sides.

8b = 30. Divide by 8 both sides .

b=30/8=3.5

ii)

11(2m+1)+12m=2+5(4-9m)

22m+11+12m=2+20-45m

Add-11+45m to both sides to make m on left and numbers on right:

22m +11+12m -11+45m = 2+20-45m -11+45m

22m+12m+45m = 11

79m = 11. Divide both sides by 79 to get m:

m = 11/79

iii)

-(3-3p)+7(-2p-6)=-7p+9-10p-12.

-3+3p-14p-42 = -7p+9-10p-12

Collect the p's and number together on each side andsimplify:

-11p - 45 =  -17p - 3.

Add 45+17p to both sides to male p's on one side and numbers on the other side:

-11p-45 +45+17p = -17p-3+45+17p

Simplify:

6p = 42. Divide both sides by 6 to get p

p = 7