(12b+7)(5b-15)=0

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Solution for (12b+7)(5b-15)=0 equation: 


Simplifying
(12b + 7)(5b + -15) = 0

Reorder the terms:
(7 + 12b)(5b + -15) = 0

Reorder the terms:
(7 + 12b)(-15 + 5b) = 0

Multiply (7 + 12b) * (-15 + 5b)
(7(-15 + 5b) + 12b * (-15 + 5b)) = 0
((-15 * 7 + 5b * 7) + 12b * (-15 + 5b)) = 0
((-105 + 35b) + 12b * (-15 + 5b)) = 0
(-105 + 35b + (-15 * 12b + 5b * 12b)) = 0
(-105 + 35b + (-180b + 60b2)) = 0

Combine like terms: 35b + -180b = -145b
(-105 + -145b + 60b2) = 0

Solving
-105 + -145b + 60b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -29b + 12b2) = 0

Factor a trinomial.
5((-7 + -12b)(3 + -1b)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -12b)' equal to zero and attempt to solve:

Simplifying
-7 + -12b = 0

Solving
-7 + -12b = 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 + -12b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12b = 0 + 7
-12b = 0 + 7

Combine like terms: 0 + 7 = 7
-12b = 7

Divide each side by '-12'.
b = -0.5833333333

Simplifying
b = -0.5833333333

Subproblem 2
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 = {-0.5833333333, 3}

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