(8b+5)(3b-7)=0

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Solution for (8b+5)(3b-7)=0 equation: 


Simplifying
(8b + 5)(3b + -7) = 0

Reorder the terms:
(5 + 8b)(3b + -7) = 0

Reorder the terms:
(5 + 8b)(-7 + 3b) = 0

Multiply (5 + 8b) * (-7 + 3b)
(5(-7 + 3b) + 8b * (-7 + 3b)) = 0
((-7 * 5 + 3b * 5) + 8b * (-7 + 3b)) = 0
((-35 + 15b) + 8b * (-7 + 3b)) = 0
(-35 + 15b + (-7 * 8b + 3b * 8b)) = 0
(-35 + 15b + (-56b + 24b2)) = 0

Combine like terms: 15b + -56b = -41b
(-35 + -41b + 24b2) = 0

Solving
-35 + -41b + 24b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -8b)(7 + -3b) = 0


Subproblem 1
Set the factor '(-5 + -8b)' equal to zero and attempt to solve:

Simplifying
-5 + -8b = 0

Solving
-5 + -8b = 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 + -8b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8b = 0 + 5
-8b = 0 + 5

Combine like terms: 0 + 5 = 5
-8b = 5

Divide each side by '-8'.
b = -0.625

Simplifying
b = -0.625

Subproblem 2
Set the factor '(7 + -3b)' equal to zero and attempt to solve:

Simplifying
7 + -3b = 0

Solving
7 + -3b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3b = 0 + -7
-3b = 0 + -7

Combine like terms: 0 + -7 = -7
-3b = -7

Divide each side by '-3'.
b = 2.333333333

Simplifying
b = 2.333333333
Solution
b = {-0.625, 2.333333333}

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