12b^2+b=6

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Solution for 12b^2+b=6 equation:


Simplifying
12b2 + b = 6

Reorder the terms:
b + 12b2 = 6

Solving
b + 12b2 = 6

Solving for variable 'b'.

Reorder the terms:
-6 + b + 12b2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + b + 12b2 = 0

Factor a trinomial.
(-3 + -4b)(2 + -3b) = 0

Subproblem 1

Set the factor '(-3 + -4b)' equal to zero and attempt to solve: Simplifying -3 + -4b = 0 Solving -3 + -4b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4b = 0 + 3 -4b = 0 + 3 Combine like terms: 0 + 3 = 3 -4b = 3 Divide each side by '-4'. b = -0.75 Simplifying b = -0.75

Subproblem 2

Set the factor '(2 + -3b)' equal to zero and attempt to solve: Simplifying 2 + -3b = 0 Solving 2 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3b = 0 + -2 -3b = 0 + -2 Combine like terms: 0 + -2 = -2 -3b = -2 Divide each side by '-3'. b = 0.6666666667 Simplifying b = 0.6666666667

Solution

b = {-0.75, 0.6666666667}

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