7b^2+42b=-56

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Solution for 7b^2+42b=-56 equation:


Simplifying
7b2 + 42b = -56

Reorder the terms:
42b + 7b2 = -56

Solving
42b + 7b2 = -56

Solving for variable 'b'.

Reorder the terms:
56 + 42b + 7b2 = -56 + 56

Combine like terms: -56 + 56 = 0
56 + 42b + 7b2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(8 + 6b + b2) = 0

Factor a trinomial.
7((4 + b)(2 + b)) = 0

Ignore the factor 7.

Subproblem 1

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

Subproblem 2

Set the factor '(2 + b)' equal to zero and attempt to solve: Simplifying 2 + b = 0 Solving 2 + b = 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 + b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + b = 0 + -2 b = 0 + -2 Combine like terms: 0 + -2 = -2 b = -2 Simplifying b = -2

Solution

b = {-4, -2}

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