b^2+5b-28=3b+7

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Solution for b^2+5b-28=3b+7 equation: 


Simplifying
b2 + 5b + -28 = 3b + 7

Reorder the terms:
-28 + 5b + b2 = 3b + 7

Reorder the terms:
-28 + 5b + b2 = 7 + 3b

Solving
-28 + 5b + b2 = 7 + 3b

Solving for variable 'b'.

Reorder the terms:
-28 + -7 + 5b + -3b + b2 = 7 + 3b + -7 + -3b

Combine like terms: -28 + -7 = -35
-35 + 5b + -3b + b2 = 7 + 3b + -7 + -3b

Combine like terms: 5b + -3b = 2b
-35 + 2b + b2 = 7 + 3b + -7 + -3b

Reorder the terms:
-35 + 2b + b2 = 7 + -7 + 3b + -3b

Combine like terms: 7 + -7 = 0
-35 + 2b + b2 = 0 + 3b + -3b
-35 + 2b + b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
-35 + 2b + b2 = 0

Factor a trinomial.
(-7 + -1b)(5 + -1b) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {-7, 5}

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