(3b+4)(2b+7)=

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Solution for (3b+4)(2b+7)= equation: 


Simplifying
(3b + 4)(2b + 7) = 0

Reorder the terms:
(4 + 3b)(2b + 7) = 0

Reorder the terms:
(4 + 3b)(7 + 2b) = 0

Multiply (4 + 3b) * (7 + 2b)
(4(7 + 2b) + 3b * (7 + 2b)) = 0
((7 * 4 + 2b * 4) + 3b * (7 + 2b)) = 0
((28 + 8b) + 3b * (7 + 2b)) = 0
(28 + 8b + (7 * 3b + 2b * 3b)) = 0
(28 + 8b + (21b + 6b2)) = 0

Combine like terms: 8b + 21b = 29b
(28 + 29b + 6b2) = 0

Solving
28 + 29b + 6b2 = 0

Solving for variable 'b'.

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


Subproblem 1
Set the factor '(7 + 2b)' equal to zero and attempt to solve:

Simplifying
7 + 2b = 0

Solving
7 + 2b = 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 + 2b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2b = 0 + -7
2b = 0 + -7

Combine like terms: 0 + -7 = -7
2b = -7

Divide each side by '2'.
b = -3.5

Simplifying
b = -3.5

Subproblem 2
Set the factor '(4 + 3b)' equal to zero and attempt to solve:

Simplifying
4 + 3b = 0

Solving
4 + 3b = 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 + 3b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3b = 0 + -4
3b = 0 + -4

Combine like terms: 0 + -4 = -4
3b = -4

Divide each side by '3'.
b = -1.333333333

Simplifying
b = -1.333333333
Solution
b = {-3.5, -1.333333333}

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