4b^2=20b+56

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Solution for 4b^2=20b+56 equation:


Simplifying
4b2 = 20b + 56

Reorder the terms:
4b2 = 56 + 20b

Solving
4b2 = 56 + 20b

Solving for variable 'b'.

Reorder the terms:
-56 + -20b + 4b2 = 56 + 20b + -56 + -20b

Reorder the terms:
-56 + -20b + 4b2 = 56 + -56 + 20b + -20b

Combine like terms: 56 + -56 = 0
-56 + -20b + 4b2 = 0 + 20b + -20b
-56 + -20b + 4b2 = 20b + -20b

Combine like terms: 20b + -20b = 0
-56 + -20b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + -5b + b2) = 0

Factor a trinomial.
4((-2 + -1b)(7 + -1b)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -1b)' equal to zero and attempt to solve: Simplifying 7 + -1b = 0 Solving 7 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1b = 0 + -7 -1b = 0 + -7 Combine like terms: 0 + -7 = -7 -1b = -7 Divide each side by '-1'. b = 7 Simplifying b = 7

Solution

b = {-2, 7}

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