(b-7)(6b+7)=0

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Solution for (b-7)(6b+7)=0 equation: 


Simplifying
(b + -7)(6b + 7) = 0

Reorder the terms:
(-7 + b)(6b + 7) = 0

Reorder the terms:
(-7 + b)(7 + 6b) = 0

Multiply (-7 + b) * (7 + 6b)
(-7(7 + 6b) + b(7 + 6b)) = 0
((7 * -7 + 6b * -7) + b(7 + 6b)) = 0
((-49 + -42b) + b(7 + 6b)) = 0
(-49 + -42b + (7 * b + 6b * b)) = 0
(-49 + -42b + (7b + 6b2)) = 0

Combine like terms: -42b + 7b = -35b
(-49 + -35b + 6b2) = 0

Solving
-49 + -35b + 6b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-7 + -6b)(7 + -1b) = 0


Subproblem 1
Set the factor '(-7 + -6b)' equal to zero and attempt to solve:

Simplifying
-7 + -6b = 0

Solving
-7 + -6b = 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 + -6b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6b = 0 + 7
-6b = 0 + 7

Combine like terms: 0 + 7 = 7
-6b = 7

Divide each side by '-6'.
b = -1.166666667

Simplifying
b = -1.166666667

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 = {-1.166666667, 7}

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