(2b-7)(2b+13)=0

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Solution for (2b-7)(2b+13)=0 equation: 


Simplifying
(2b + -7)(2b + 13) = 0

Reorder the terms:
(-7 + 2b)(2b + 13) = 0

Reorder the terms:
(-7 + 2b)(13 + 2b) = 0

Multiply (-7 + 2b) * (13 + 2b)
(-7(13 + 2b) + 2b * (13 + 2b)) = 0
((13 * -7 + 2b * -7) + 2b * (13 + 2b)) = 0
((-91 + -14b) + 2b * (13 + 2b)) = 0
(-91 + -14b + (13 * 2b + 2b * 2b)) = 0
(-91 + -14b + (26b + 4b2)) = 0

Combine like terms: -14b + 26b = 12b
(-91 + 12b + 4b2) = 0

Solving
-91 + 12b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-13 + -2b)(7 + -2b) = 0


Subproblem 1
Set the factor '(-13 + -2b)' equal to zero and attempt to solve:

Simplifying
-13 + -2b = 0

Solving
-13 + -2b = 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 + -2b = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2b = 0 + 13
-2b = 0 + 13

Combine like terms: 0 + 13 = 13
-2b = 13

Divide each side by '-2'.
b = -6.5

Simplifying
b = -6.5

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

Simplifying
7 + -2b = 0

Solving
7 + -2b = 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 + -2b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2b = 0 + -7
-2b = 0 + -7

Combine like terms: 0 + -7 = -7
-2b = -7

Divide each side by '-2'.
b = 3.5

Simplifying
b = 3.5
Solution
b = {-6.5, 3.5}

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