4b^2-24b-59=5

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Solution for 4b^2-24b-59=5 equation: 


Simplifying
4b2 + -24b + -59 = 5

Reorder the terms:
-59 + -24b + 4b2 = 5

Solving
-59 + -24b + 4b2 = 5

Solving for variable 'b'.

Reorder the terms:
-59 + -5 + -24b + 4b2 = 5 + -5

Combine like terms: -59 + -5 = -64
-64 + -24b + 4b2 = 5 + -5

Combine like terms: 5 + -5 = 0
-64 + -24b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -6b + b2) = 0

Factor a trinomial.
4((-2 + -1b)(8 + -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 '(8 + -1b)' equal to zero and attempt to solve:

Simplifying
8 + -1b = 0

Solving
8 + -1b = 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 + -1b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1b = 0 + -8
-1b = 0 + -8

Combine like terms: 0 + -8 = -8
-1b = -8

Divide each side by '-1'.
b = 8

Simplifying
b = 8
Solution
b = {-2, 8}

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