(3b-7)(5b-10)=0

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Solution for (3b-7)(5b-10)=0 equation: 


Simplifying
(3b + -7)(5b + -10) = 0

Reorder the terms:
(-7 + 3b)(5b + -10) = 0

Reorder the terms:
(-7 + 3b)(-10 + 5b) = 0

Multiply (-7 + 3b) * (-10 + 5b)
(-7(-10 + 5b) + 3b * (-10 + 5b)) = 0
((-10 * -7 + 5b * -7) + 3b * (-10 + 5b)) = 0
((70 + -35b) + 3b * (-10 + 5b)) = 0
(70 + -35b + (-10 * 3b + 5b * 3b)) = 0
(70 + -35b + (-30b + 15b2)) = 0

Combine like terms: -35b + -30b = -65b
(70 + -65b + 15b2) = 0

Solving
70 + -65b + 15b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(14 + -13b + 3b2) = 0

Factor a trinomial.
5((2 + -1b)(7 + -3b)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2

Subproblem 2
Set the factor '(7 + -3b)' equal to zero and attempt to solve:

Simplifying
7 + -3b = 0

Solving
7 + -3b = 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 + -3b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3b = 0 + -7
-3b = 0 + -7

Combine like terms: 0 + -7 = -7
-3b = -7

Divide each side by '-3'.
b = 2.333333333

Simplifying
b = 2.333333333
Solution
b = {2, 2.333333333}

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