b(13b+7)(6b-18)=0

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Solution for b(13b+7)(6b-18)=0 equation: 


Simplifying
b(13b + 7)(6b + -18) = 0

Reorder the terms:
b(7 + 13b)(6b + -18) = 0

Reorder the terms:
b(7 + 13b)(-18 + 6b) = 0

Multiply (7 + 13b) * (-18 + 6b)
b(7(-18 + 6b) + 13b * (-18 + 6b)) = 0
b((-18 * 7 + 6b * 7) + 13b * (-18 + 6b)) = 0
b((-126 + 42b) + 13b * (-18 + 6b)) = 0
b(-126 + 42b + (-18 * 13b + 6b * 13b)) = 0
b(-126 + 42b + (-234b + 78b2)) = 0

Combine like terms: 42b + -234b = -192b
b(-126 + -192b + 78b2) = 0
(-126 * b + -192b * b + 78b2 * b) = 0
(-126b + -192b2 + 78b3) = 0

Solving
-126b + -192b2 + 78b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6b'.
6b(-21 + -32b + 13b2) = 0

Factor a trinomial.
6b((-7 + -13b)(3 + -1b)) = 0

Ignore the factor 6.

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 '(-7 + -13b)' equal to zero and attempt to solve:

Simplifying
-7 + -13b = 0

Solving
-7 + -13b = 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 + -13b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13b = 0 + 7
-13b = 0 + 7

Combine like terms: 0 + 7 = 7
-13b = 7

Divide each side by '-13'.
b = -0.5384615385

Simplifying
b = -0.5384615385

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

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {0, -0.5384615385, 3}

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