14b^2-28b=2b-16

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Solution for 14b^2-28b=2b-16 equation: 


Simplifying
14b2 + -28b = 2b + -16

Reorder the terms:
-28b + 14b2 = 2b + -16

Reorder the terms:
-28b + 14b2 = -16 + 2b

Solving
-28b + 14b2 = -16 + 2b

Solving for variable 'b'.

Reorder the terms:
16 + -28b + -2b + 14b2 = -16 + 2b + 16 + -2b

Combine like terms: -28b + -2b = -30b
16 + -30b + 14b2 = -16 + 2b + 16 + -2b

Reorder the terms:
16 + -30b + 14b2 = -16 + 16 + 2b + -2b

Combine like terms: -16 + 16 = 0
16 + -30b + 14b2 = 0 + 2b + -2b
16 + -30b + 14b2 = 2b + -2b

Combine like terms: 2b + -2b = 0
16 + -30b + 14b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -15b + 7b2) = 0

Factor a trinomial.
2((1 + -1b)(8 + -7b)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

Simplifying
b = 1

Subproblem 2
Set the factor '(8 + -7b)' equal to zero and attempt to solve:

Simplifying
8 + -7b = 0

Solving
8 + -7b = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7b = 0 + -8
-7b = 0 + -8

Combine like terms: 0 + -8 = -8
-7b = -8

Divide each side by '-7'.
b = 1.142857143

Simplifying
b = 1.142857143
Solution
b = {1, 1.142857143}

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