(6-3b)(6-b)(6+b)(6+3b)=945

Solution for (6-3b)(6-b)(6+b)(6+3b)=945 equation:

Simplifying
(6 + -3b)(6 + -1b)(6 + b)(6 + 3b) = 945

Multiply (6 + -3b) * (6 + -1b)
(6(6 + -1b) + -3b * (6 + -1b))(6 + b)(6 + 3b) = 945
((6 * 6 + -1b * 6) + -3b * (6 + -1b))(6 + b)(6 + 3b) = 945
((36 + -6b) + -3b * (6 + -1b))(6 + b)(6 + 3b) = 945
(36 + -6b + (6 * -3b + -1b * -3b))(6 + b)(6 + 3b) = 945
(36 + -6b + (-18b + 3b2))(6 + b)(6 + 3b) = 945

Combine like terms: -6b + -18b = -24b
(36 + -24b + 3b2)(6 + b)(6 + 3b) = 945

Multiply (36 + -24b + 3b2) * (6 + b)
(36(6 + b) + -24b * (6 + b) + 3b2 * (6 + b))(6 + 3b) = 945
((6 * 36 + b * 36) + -24b * (6 + b) + 3b2 * (6 + b))(6 + 3b) = 945
((216 + 36b) + -24b * (6 + b) + 3b2 * (6 + b))(6 + 3b) = 945
(216 + 36b + (6 * -24b + b * -24b) + 3b2 * (6 + b))(6 + 3b) = 945
(216 + 36b + (-144b + -24b2) + 3b2 * (6 + b))(6 + 3b) = 945
(216 + 36b + -144b + -24b2 + (6 * 3b2 + b * 3b2))(6 + 3b) = 945
(216 + 36b + -144b + -24b2 + (18b2 + 3b3))(6 + 3b) = 945

Combine like terms: 36b + -144b = -108b
(216 + -108b + -24b2 + 18b2 + 3b3)(6 + 3b) = 945

Combine like terms: -24b2 + 18b2 = -6b2
(216 + -108b + -6b2 + 3b3)(6 + 3b) = 945

Multiply (216 + -108b + -6b2 + 3b3) * (6 + 3b)
(216(6 + 3b) + -108b * (6 + 3b) + -6b2 * (6 + 3b) + 3b3 * (6 + 3b)) = 945
((6 * 216 + 3b * 216) + -108b * (6 + 3b) + -6b2 * (6 + 3b) + 3b3 * (6 + 3b)) = 945
((1296 + 648b) + -108b * (6 + 3b) + -6b2 * (6 + 3b) + 3b3 * (6 + 3b)) = 945
(1296 + 648b + (6 * -108b + 3b * -108b) + -6b2 * (6 + 3b) + 3b3 * (6 + 3b)) = 945
(1296 + 648b + (-648b + -324b2) + -6b2 * (6 + 3b) + 3b3 * (6 + 3b)) = 945
(1296 + 648b + -648b + -324b2 + (6 * -6b2 + 3b * -6b2) + 3b3 * (6 + 3b)) = 945
(1296 + 648b + -648b + -324b2 + (-36b2 + -18b3) + 3b3 * (6 + 3b)) = 945
(1296 + 648b + -648b + -324b2 + -36b2 + -18b3 + (6 * 3b3 + 3b * 3b3)) = 945
(1296 + 648b + -648b + -324b2 + -36b2 + -18b3 + (18b3 + 9b4)) = 945

Combine like terms: 648b + -648b = 0
(1296 + 0 + -324b2 + -36b2 + -18b3 + 18b3 + 9b4) = 945
(1296 + -324b2 + -36b2 + -18b3 + 18b3 + 9b4) = 945

Combine like terms: -324b2 + -36b2 = -360b2
(1296 + -360b2 + -18b3 + 18b3 + 9b4) = 945

Combine like terms: -18b3 + 18b3 = 0
(1296 + -360b2 + 0 + 9b4) = 945
(1296 + -360b2 + 9b4) = 945

Solving
1296 + -360b2 + 9b4 = 945

Solving for variable 'b'.

Reorder the terms:
1296 + -945 + -360b2 + 9b4 = 945 + -945

Combine like terms: 1296 + -945 = 351
351 + -360b2 + 9b4 = 945 + -945

Combine like terms: 945 + -945 = 0
351 + -360b2 + 9b4 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(39 + -40b2 + b4) = 0

Factor a trinomial.
9((1 + -1b2)(39 + -1b2)) = 0

Factor a difference between two squares.
9(((1 + b)(1 + -1b))(39 + -1b2)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(39 + -1b2)' equal to zero and attempt to solve:

Simplifying
39 + -1b2 = 0

Solving
39 + -1b2 = 0

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

Add '-39' to each side of the equation.
39 + -39 + -1b2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -1b2 = 0 + -39
-1b2 = 0 + -39

Combine like terms: 0 + -39 = -39
-1b2 = -39

Divide each side by '-1'.
b2 = 39

Simplifying
b2 = 39

Take the square root of each side:
b = {-6.244997998, 6.244997998}
Subproblem 2
Set the factor '(1 + b)' equal to zero and attempt to solve:

Simplifying
1 + b = 0

Solving
1 + b = 0

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

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

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

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

Simplifying
b = -1
Subproblem 3
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

Simplifying
b = 1
Solution
b = {-6.244997998, 6.244997998, -1, 1}