(30-b)*(30-b)+b*b=900

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Solution for (30-b)*(30-b)+b*b=900 equation: 


Simplifying
(30 + -1b)(30 + -1b) + b * b = 900

Multiply (30 + -1b) * (30 + -1b)
(30(30 + -1b) + -1b * (30 + -1b)) + b * b = 900
((30 * 30 + -1b * 30) + -1b * (30 + -1b)) + b * b = 900
((900 + -30b) + -1b * (30 + -1b)) + b * b = 900
(900 + -30b + (30 * -1b + -1b * -1b)) + b * b = 900
(900 + -30b + (-30b + 1b2)) + b * b = 900

Combine like terms: -30b + -30b = -60b
(900 + -60b + 1b2) + b * b = 900

Multiply b * b
900 + -60b + 1b2 + b2 = 900

Combine like terms: 1b2 + b2 = 2b2
900 + -60b + 2b2 = 900

Add '-900' to each side of the equation.
900 + -60b + -900 + 2b2 = 900 + -900

Reorder the terms:
900 + -900 + -60b + 2b2 = 900 + -900

Combine like terms: 900 + -900 = 0
0 + -60b + 2b2 = 900 + -900
-60b + 2b2 = 900 + -900

Combine like terms: 900 + -900 = 0
-60b + 2b2 = 0

Solving
-60b + 2b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2b'.
2b(-30 + b) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

Move all terms containing b to the left, all other terms to the right.

Simplifying
b = 0

Subproblem 2
Set the factor '(-30 + b)' equal to zero and attempt to solve:

Simplifying
-30 + b = 0

Solving
-30 + b = 0

Move all terms containing b to the left, all other terms to the right.

Add '30' to each side of the equation.
-30 + 30 + b = 0 + 30

Combine like terms: -30 + 30 = 0
0 + b = 0 + 30
b = 0 + 30

Combine like terms: 0 + 30 = 30
b = 30

Simplifying
b = 30
Solution
b = {0, 30}

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