11b^2+134b+242=-4b-7b^2+2

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Solution for 11b^2+134b+242=-4b-7b^2+2 equation: 


Simplifying
11b2 + 134b + 242 = -4b + -7b2 + 2

Reorder the terms:
242 + 134b + 11b2 = -4b + -7b2 + 2

Reorder the terms:
242 + 134b + 11b2 = 2 + -4b + -7b2

Solving
242 + 134b + 11b2 = 2 + -4b + -7b2

Solving for variable 'b'.

Reorder the terms:
242 + -2 + 134b + 4b + 11b2 + 7b2 = 2 + -4b + -7b2 + -2 + 4b + 7b2

Combine like terms: 242 + -2 = 240
240 + 134b + 4b + 11b2 + 7b2 = 2 + -4b + -7b2 + -2 + 4b + 7b2

Combine like terms: 134b + 4b = 138b
240 + 138b + 11b2 + 7b2 = 2 + -4b + -7b2 + -2 + 4b + 7b2

Combine like terms: 11b2 + 7b2 = 18b2
240 + 138b + 18b2 = 2 + -4b + -7b2 + -2 + 4b + 7b2

Reorder the terms:
240 + 138b + 18b2 = 2 + -2 + -4b + 4b + -7b2 + 7b2

Combine like terms: 2 + -2 = 0
240 + 138b + 18b2 = 0 + -4b + 4b + -7b2 + 7b2
240 + 138b + 18b2 = -4b + 4b + -7b2 + 7b2

Combine like terms: -4b + 4b = 0
240 + 138b + 18b2 = 0 + -7b2 + 7b2
240 + 138b + 18b2 = -7b2 + 7b2

Combine like terms: -7b2 + 7b2 = 0
240 + 138b + 18b2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(40 + 23b + 3b2) = 0

Factor a trinomial.
6((5 + b)(8 + 3b)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(5 + b)' equal to zero and attempt to solve:

Simplifying
5 + b = 0

Solving
5 + b = 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 + b = 0 + -5

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

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

Simplifying
b = -5

Subproblem 2
Set the factor '(8 + 3b)' equal to zero and attempt to solve:

Simplifying
8 + 3b = 0

Solving
8 + 3b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + 3b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3b = 0 + -8
3b = 0 + -8

Combine like terms: 0 + -8 = -8
3b = -8

Divide each side by '3'.
b = -2.666666667

Simplifying
b = -2.666666667
Solution
b = {-5, -2.666666667}

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