6b^2=15+27b

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Solution for 6b^2=15+27b equation:


Simplifying
6b2 = 15 + 27b

Solving
6b2 = 15 + 27b

Solving for variable 'b'.

Reorder the terms:
-15 + -27b + 6b2 = 15 + 27b + -15 + -27b

Reorder the terms:
-15 + -27b + 6b2 = 15 + -15 + 27b + -27b

Combine like terms: 15 + -15 = 0
-15 + -27b + 6b2 = 0 + 27b + -27b
-15 + -27b + 6b2 = 27b + -27b

Combine like terms: 27b + -27b = 0
-15 + -27b + 6b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -9b + 2b2) = 0

Factor a trinomial.
3((-1 + -2b)(5 + -1b)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + -2b)' equal to zero and attempt to solve: Simplifying -1 + -2b = 0 Solving -1 + -2b = 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 + -2b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2b = 0 + 1 -2b = 0 + 1 Combine like terms: 0 + 1 = 1 -2b = 1 Divide each side by '-2'. b = -0.5 Simplifying b = -0.5

Subproblem 2

Set the factor '(5 + -1b)' equal to zero and attempt to solve: Simplifying 5 + -1b = 0 Solving 5 + -1b = 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 + -1b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1b = 0 + -5 -1b = 0 + -5 Combine like terms: 0 + -5 = -5 -1b = -5 Divide each side by '-1'. b = 5 Simplifying b = 5

Solution

b = {-0.5, 5}

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