3b(2b+5)=5b(7b-21)

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Solution for 3b(2b+5)=5b(7b-21) equation: 


Simplifying
3b(2b + 5) = 5b(7b + -21)

Reorder the terms:
3b(5 + 2b) = 5b(7b + -21)
(5 * 3b + 2b * 3b) = 5b(7b + -21)
(15b + 6b2) = 5b(7b + -21)

Reorder the terms:
15b + 6b2 = 5b(-21 + 7b)
15b + 6b2 = (-21 * 5b + 7b * 5b)
15b + 6b2 = (-105b + 35b2)

Solving
15b + 6b2 = -105b + 35b2

Solving for variable 'b'.

Reorder the terms:
15b + 105b + 6b2 + -35b2 = -105b + 35b2 + 105b + -35b2

Combine like terms: 15b + 105b = 120b
120b + 6b2 + -35b2 = -105b + 35b2 + 105b + -35b2

Combine like terms: 6b2 + -35b2 = -29b2
120b + -29b2 = -105b + 35b2 + 105b + -35b2

Reorder the terms:
120b + -29b2 = -105b + 105b + 35b2 + -35b2

Combine like terms: -105b + 105b = 0
120b + -29b2 = 0 + 35b2 + -35b2
120b + -29b2 = 35b2 + -35b2

Combine like terms: 35b2 + -35b2 = 0
120b + -29b2 = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(120 + -29b) = 0


Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0

Subproblem 2
Set the factor '(120 + -29b)' equal to zero and attempt to solve:

Simplifying
120 + -29b = 0

Solving
120 + -29b = 0

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

Add '-120' to each side of the equation.
120 + -120 + -29b = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -29b = 0 + -120
-29b = 0 + -120

Combine like terms: 0 + -120 = -120
-29b = -120

Divide each side by '-29'.
b = 4.137931034

Simplifying
b = 4.137931034
Solution
b = {0, 4.137931034}

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