0=(b-8)(b-8)+(b^2)-1600

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Solution for 0=(b-8)(b-8)+(b^2)-1600 equation: 


Simplifying
0 = (b + -8)(b + -8) + (b2) + -1600

Reorder the terms:
0 = (-8 + b)(b + -8) + (b2) + -1600

Reorder the terms:
0 = (-8 + b)(-8 + b) + (b2) + -1600

Multiply (-8 + b) * (-8 + b)
0 = (-8(-8 + b) + b(-8 + b)) + (b2) + -1600
0 = ((-8 * -8 + b * -8) + b(-8 + b)) + (b2) + -1600
0 = ((64 + -8b) + b(-8 + b)) + (b2) + -1600
0 = (64 + -8b + (-8 * b + b * b)) + (b2) + -1600
0 = (64 + -8b + (-8b + b2)) + (b2) + -1600

Combine like terms: -8b + -8b = -16b
0 = (64 + -16b + b2) + (b2) + -1600
0 = 64 + -16b + b2 + b2 + -1600

Reorder the terms:
0 = 64 + -1600 + -16b + b2 + b2

Combine like terms: 64 + -1600 = -1536
0 = -1536 + -16b + b2 + b2

Combine like terms: b2 + b2 = 2b2
0 = -1536 + -16b + 2b2

Solving
0 = -1536 + -16b + 2b2

Solving for variable 'b'.

Combine like terms: 0 + 1536 = 1536
1536 + 16b + -2b2 = -1536 + -16b + 2b2 + 1536 + 16b + -2b2

Reorder the terms:
1536 + 16b + -2b2 = -1536 + 1536 + -16b + 16b + 2b2 + -2b2

Combine like terms: -1536 + 1536 = 0
1536 + 16b + -2b2 = 0 + -16b + 16b + 2b2 + -2b2
1536 + 16b + -2b2 = -16b + 16b + 2b2 + -2b2

Combine like terms: -16b + 16b = 0
1536 + 16b + -2b2 = 0 + 2b2 + -2b2
1536 + 16b + -2b2 = 2b2 + -2b2

Combine like terms: 2b2 + -2b2 = 0
1536 + 16b + -2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(768 + 8b + -1b2) = 0

Factor a trinomial.
2((32 + -1b)(24 + b)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(32 + -1b)' equal to zero and attempt to solve:

Simplifying
32 + -1b = 0

Solving
32 + -1b = 0

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

Add '-32' to each side of the equation.
32 + -32 + -1b = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -1b = 0 + -32
-1b = 0 + -32

Combine like terms: 0 + -32 = -32
-1b = -32

Divide each side by '-1'.
b = 32

Simplifying
b = 32

Subproblem 2
Set the factor '(24 + b)' equal to zero and attempt to solve:

Simplifying
24 + b = 0

Solving
24 + b = 0

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

Add '-24' to each side of the equation.
24 + -24 + b = 0 + -24

Combine like terms: 24 + -24 = 0
0 + b = 0 + -24
b = 0 + -24

Combine like terms: 0 + -24 = -24
b = -24

Simplifying
b = -24
Solution
b = {32, -24}

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