0=7b-6-b^2

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Solution for 0=7b-6-b^2 equation:


Simplifying
0 = 7b + -6 + -1b2

Reorder the terms:
0 = -6 + 7b + -1b2

Solving
0 = -6 + 7b + -1b2

Solving for variable 'b'.

Combine like terms: 0 + 6 = 6
6 + -7b + b2 = -6 + 7b + -1b2 + 6 + -7b + b2

Reorder the terms:
6 + -7b + b2 = -6 + 6 + 7b + -7b + -1b2 + b2

Combine like terms: -6 + 6 = 0
6 + -7b + b2 = 0 + 7b + -7b + -1b2 + b2
6 + -7b + b2 = 7b + -7b + -1b2 + b2

Combine like terms: 7b + -7b = 0
6 + -7b + b2 = 0 + -1b2 + b2
6 + -7b + b2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
6 + -7b + b2 = 0

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

Subproblem 1

Set the factor '(1 + -1b)' equal to zero and attempt to solve: Simplifying 1 + -1b = 0 Solving 1 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1b = 0 + -1 -1b = 0 + -1 Combine like terms: 0 + -1 = -1 -1b = -1 Divide each side by '-1'. b = 1 Simplifying b = 1

Subproblem 2

Set the factor '(6 + -1b)' equal to zero and attempt to solve: Simplifying 6 + -1b = 0 Solving 6 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1b = 0 + -6 -1b = 0 + -6 Combine like terms: 0 + -6 = -6 -1b = -6 Divide each side by '-1'. b = 6 Simplifying b = 6

Solution

b = {1, 6}

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