(3b+7)(2b-5)=0

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Solution for (3b+7)(2b-5)=0 equation: 


Simplifying
(3b + 7)(2b + -5) = 0

Reorder the terms:
(7 + 3b)(2b + -5) = 0

Reorder the terms:
(7 + 3b)(-5 + 2b) = 0

Multiply (7 + 3b) * (-5 + 2b)
(7(-5 + 2b) + 3b * (-5 + 2b)) = 0
((-5 * 7 + 2b * 7) + 3b * (-5 + 2b)) = 0
((-35 + 14b) + 3b * (-5 + 2b)) = 0
(-35 + 14b + (-5 * 3b + 2b * 3b)) = 0
(-35 + 14b + (-15b + 6b2)) = 0

Combine like terms: 14b + -15b = -1b
(-35 + -1b + 6b2) = 0

Solving
-35 + -1b + 6b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-7 + -3b)(5 + -2b) = 0


Subproblem 1
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

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

Simplifying
5 + -2b = 0

Solving
5 + -2b = 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 + -2b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2b = 0 + -5
-2b = 0 + -5

Combine like terms: 0 + -5 = -5
-2b = -5

Divide each side by '-2'.
b = 2.5

Simplifying
b = 2.5
Solution
b = {-2.333333333, 2.5}

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