b(b+20)=8(4+3b)

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Solution for b(b+20)=8(4+3b) equation: 


Simplifying
b(b + 20) = 8(4 + 3b)

Reorder the terms:
b(20 + b) = 8(4 + 3b)
(20 * b + b * b) = 8(4 + 3b)
(20b + b2) = 8(4 + 3b)
20b + b2 = (4 * 8 + 3b * 8)
20b + b2 = (32 + 24b)

Solving
20b + b2 = 32 + 24b

Solving for variable 'b'.

Reorder the terms:
-32 + 20b + -24b + b2 = 32 + 24b + -32 + -24b

Combine like terms: 20b + -24b = -4b
-32 + -4b + b2 = 32 + 24b + -32 + -24b

Reorder the terms:
-32 + -4b + b2 = 32 + -32 + 24b + -24b

Combine like terms: 32 + -32 = 0
-32 + -4b + b2 = 0 + 24b + -24b
-32 + -4b + b2 = 24b + -24b

Combine like terms: 24b + -24b = 0
-32 + -4b + b2 = 0

Factor a trinomial.
(-4 + -1b)(8 + -1b) = 0


Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve:

Simplifying
-4 + -1b = 0

Solving
-4 + -1b = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1b = 0 + 4
-1b = 0 + 4

Combine like terms: 0 + 4 = 4
-1b = 4

Divide each side by '-1'.
b = -4

Simplifying
b = -4

Subproblem 2
Set the factor '(8 + -1b)' equal to zero and attempt to solve:

Simplifying
8 + -1b = 0

Solving
8 + -1b = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1b = 0 + -8
-1b = 0 + -8

Combine like terms: 0 + -8 = -8
-1b = -8

Divide each side by '-1'.
b = 8

Simplifying
b = 8
Solution
b = {-4, 8}

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