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

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


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

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

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

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

Combine like terms: 5b + -14b = -9b
(-35 + -9b + 2b2) = 0

Solving
-35 + -9b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -2b)(7 + -1b) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 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 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {-2.5, 7}

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