b^2=6-5b

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Solution for b^2=6-5b equation:


Simplifying
b2 = 6 + -5b

Solving
b2 = 6 + -5b

Solving for variable 'b'.

Reorder the terms:
-6 + 5b + b2 = 6 + -5b + -6 + 5b

Reorder the terms:
-6 + 5b + b2 = 6 + -6 + -5b + 5b

Combine like terms: 6 + -6 = 0
-6 + 5b + b2 = 0 + -5b + 5b
-6 + 5b + b2 = -5b + 5b

Combine like terms: -5b + 5b = 0
-6 + 5b + b2 = 0

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

Subproblem 1

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

Subproblem 2

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

Solution

b = {-6, 1}

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