3b(b+6)=b-10

Solution for 3b(b+6)=b-10 equation:

Simplifying
3b(b + 6) = b + -10

Reorder the terms:
3b(6 + b) = b + -10
(6 * 3b + b * 3b) = b + -10
(18b + 3b2) = b + -10

Reorder the terms:
18b + 3b2 = -10 + b

Solving
18b + 3b2 = -10 + b

Solving for variable 'b'.

Reorder the terms:
10 + 18b + -1b + 3b2 = -10 + b + 10 + -1b

Combine like terms: 18b + -1b = 17b
10 + 17b + 3b2 = -10 + b + 10 + -1b

Reorder the terms:
10 + 17b + 3b2 = -10 + 10 + b + -1b

Combine like terms: -10 + 10 = 0
10 + 17b + 3b2 = 0 + b + -1b
10 + 17b + 3b2 = b + -1b

Combine like terms: b + -1b = 0
10 + 17b + 3b2 = 0

Factor a trinomial.
(5 + b)(2 + 3b) = 0

Subproblem 1
Set the factor '(5 + b)' equal to zero and attempt to solve:

Simplifying
5 + b = 0

Solving
5 + b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + b = 0 + -5
b = 0 + -5

Combine like terms: 0 + -5 = -5
b = -5

Simplifying
b = -5
Subproblem 2
Set the factor '(2 + 3b)' equal to zero and attempt to solve:

Simplifying
2 + 3b = 0

Solving
2 + 3b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3b = 0 + -2
3b = 0 + -2

Combine like terms: 0 + -2 = -2
3b = -2

Divide each side by '3'.
b = -0.6666666667

Simplifying
b = -0.6666666667
Solution
b = {-5, -0.6666666667}