(9b-13)(4b-9)=0

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Solution for (9b-13)(4b-9)=0 equation: 


Simplifying
(9b + -13)(4b + -9) = 0

Reorder the terms:
(-13 + 9b)(4b + -9) = 0

Reorder the terms:
(-13 + 9b)(-9 + 4b) = 0

Multiply (-13 + 9b) * (-9 + 4b)
(-13(-9 + 4b) + 9b * (-9 + 4b)) = 0
((-9 * -13 + 4b * -13) + 9b * (-9 + 4b)) = 0
((117 + -52b) + 9b * (-9 + 4b)) = 0
(117 + -52b + (-9 * 9b + 4b * 9b)) = 0
(117 + -52b + (-81b + 36b2)) = 0

Combine like terms: -52b + -81b = -133b
(117 + -133b + 36b2) = 0

Solving
117 + -133b + 36b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(13 + -9b)(9 + -4b) = 0


Subproblem 1
Set the factor '(13 + -9b)' equal to zero and attempt to solve:

Simplifying
13 + -9b = 0

Solving
13 + -9b = 0

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

Add '-13' to each side of the equation.
13 + -13 + -9b = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -9b = 0 + -13
-9b = 0 + -13

Combine like terms: 0 + -13 = -13
-9b = -13

Divide each side by '-9'.
b = 1.444444444

Simplifying
b = 1.444444444

Subproblem 2
Set the factor '(9 + -4b)' equal to zero and attempt to solve:

Simplifying
9 + -4b = 0

Solving
9 + -4b = 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 + -4b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4b = 0 + -9
-4b = 0 + -9

Combine like terms: 0 + -9 = -9
-4b = -9

Divide each side by '-4'.
b = 2.25

Simplifying
b = 2.25
Solution
b = {1.444444444, 2.25}

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