b^2+10b=75

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Solution for b^2+10b=75 equation:


Simplifying
b2 + 10b = 75

Reorder the terms:
10b + b2 = 75

Solving
10b + b2 = 75

Solving for variable 'b'.

Reorder the terms:
-75 + 10b + b2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + 10b + b2 = 0

Factor a trinomial.
(-15 + -1b)(5 + -1b) = 0

Subproblem 1

Set the factor '(-15 + -1b)' equal to zero and attempt to solve: Simplifying -15 + -1b = 0 Solving -15 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1b = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1b = 0 + 15 -1b = 0 + 15 Combine like terms: 0 + 15 = 15 -1b = 15 Divide each side by '-1'. b = -15 Simplifying b = -15

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 = {-15, 5}

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