b(b+32)=9(5+4b)

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Solution for b(b+32)=9(5+4b) equation:


Simplifying
b(b + 32) = 9(5 + 4b)

Reorder the terms:
b(32 + b) = 9(5 + 4b)
(32 * b + b * b) = 9(5 + 4b)
(32b + b2) = 9(5 + 4b)
32b + b2 = (5 * 9 + 4b * 9)
32b + b2 = (45 + 36b)

Solving
32b + b2 = 45 + 36b

Solving for variable 'b'.

Reorder the terms:
-45 + 32b + -36b + b2 = 45 + 36b + -45 + -36b

Combine like terms: 32b + -36b = -4b
-45 + -4b + b2 = 45 + 36b + -45 + -36b

Reorder the terms:
-45 + -4b + b2 = 45 + -45 + 36b + -36b

Combine like terms: 45 + -45 = 0
-45 + -4b + b2 = 0 + 36b + -36b
-45 + -4b + b2 = 36b + -36b

Combine like terms: 36b + -36b = 0
-45 + -4b + b2 = 0

Factor a trinomial.
(-5 + -1b)(9 + -1b) = 0

Subproblem 1

Set the factor '(-5 + -1b)' equal to zero and attempt to solve: Simplifying -5 + -1b = 0 Solving -5 + -1b = 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 + -1b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1b = 0 + 5 -1b = 0 + 5 Combine like terms: 0 + 5 = 5 -1b = 5 Divide each side by '-1'. b = -5 Simplifying b = -5

Subproblem 2

Set the factor '(9 + -1b)' equal to zero and attempt to solve: Simplifying 9 + -1b = 0 Solving 9 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1b = 0 + -9 -1b = 0 + -9 Combine like terms: 0 + -9 = -9 -1b = -9 Divide each side by '-1'. b = 9 Simplifying b = 9

Solution

b = {-5, 9}

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