(2b-8)(3b-7)=0

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Solution for (2b-8)(3b-7)=0 equation: 


Simplifying
(2b + -8)(3b + -7) = 0

Reorder the terms:
(-8 + 2b)(3b + -7) = 0

Reorder the terms:
(-8 + 2b)(-7 + 3b) = 0

Multiply (-8 + 2b) * (-7 + 3b)
(-8(-7 + 3b) + 2b * (-7 + 3b)) = 0
((-7 * -8 + 3b * -8) + 2b * (-7 + 3b)) = 0
((56 + -24b) + 2b * (-7 + 3b)) = 0
(56 + -24b + (-7 * 2b + 3b * 2b)) = 0
(56 + -24b + (-14b + 6b2)) = 0

Combine like terms: -24b + -14b = -38b
(56 + -38b + 6b2) = 0

Solving
56 + -38b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -19b + 3b2) = 0

Factor a trinomial.
2((7 + -3b)(4 + -1b)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {2.333333333, 4}

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