(3b+11)(7b+4)-(5b-10)(3b+11)=0

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Solution for (3b+11)(7b+4)-(5b-10)(3b+11)=0 equation: 


Simplifying
(3b + 11)(7b + 4) + -1(5b + -10)(3b + 11) = 0

Reorder the terms:
(11 + 3b)(7b + 4) + -1(5b + -10)(3b + 11) = 0

Reorder the terms:
(11 + 3b)(4 + 7b) + -1(5b + -10)(3b + 11) = 0

Multiply (11 + 3b) * (4 + 7b)
(11(4 + 7b) + 3b * (4 + 7b)) + -1(5b + -10)(3b + 11) = 0
((4 * 11 + 7b * 11) + 3b * (4 + 7b)) + -1(5b + -10)(3b + 11) = 0
((44 + 77b) + 3b * (4 + 7b)) + -1(5b + -10)(3b + 11) = 0
(44 + 77b + (4 * 3b + 7b * 3b)) + -1(5b + -10)(3b + 11) = 0
(44 + 77b + (12b + 21b2)) + -1(5b + -10)(3b + 11) = 0

Combine like terms: 77b + 12b = 89b
(44 + 89b + 21b2) + -1(5b + -10)(3b + 11) = 0

Reorder the terms:
44 + 89b + 21b2 + -1(-10 + 5b)(3b + 11) = 0

Reorder the terms:
44 + 89b + 21b2 + -1(-10 + 5b)(11 + 3b) = 0

Multiply (-10 + 5b) * (11 + 3b)
44 + 89b + 21b2 + -1(-10(11 + 3b) + 5b * (11 + 3b)) = 0
44 + 89b + 21b2 + -1((11 * -10 + 3b * -10) + 5b * (11 + 3b)) = 0
44 + 89b + 21b2 + -1((-110 + -30b) + 5b * (11 + 3b)) = 0
44 + 89b + 21b2 + -1(-110 + -30b + (11 * 5b + 3b * 5b)) = 0
44 + 89b + 21b2 + -1(-110 + -30b + (55b + 15b2)) = 0

Combine like terms: -30b + 55b = 25b
44 + 89b + 21b2 + -1(-110 + 25b + 15b2) = 0
44 + 89b + 21b2 + (-110 * -1 + 25b * -1 + 15b2 * -1) = 0
44 + 89b + 21b2 + (110 + -25b + -15b2) = 0

Reorder the terms:
44 + 110 + 89b + -25b + 21b2 + -15b2 = 0

Combine like terms: 44 + 110 = 154
154 + 89b + -25b + 21b2 + -15b2 = 0

Combine like terms: 89b + -25b = 64b
154 + 64b + 21b2 + -15b2 = 0

Combine like terms: 21b2 + -15b2 = 6b2
154 + 64b + 6b2 = 0

Solving
154 + 64b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(77 + 32b + 3b2) = 0

Factor a trinomial.
2((7 + b)(11 + 3b)) = 0

Ignore the factor 2.

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

Simplifying
7 + b = 0

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

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

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

Simplifying
b = -7

Subproblem 2
Set the factor '(11 + 3b)' equal to zero and attempt to solve:

Simplifying
11 + 3b = 0

Solving
11 + 3b = 0

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

Add '-11' to each side of the equation.
11 + -11 + 3b = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 3b = 0 + -11
3b = 0 + -11

Combine like terms: 0 + -11 = -11
3b = -11

Divide each side by '3'.
b = -3.666666667

Simplifying
b = -3.666666667
Solution
b = {-7, -3.666666667}

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