14y(y-2)+11=14y-17

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Solution for 14y(y-2)+11=14y-17 equation: 


Simplifying
14y(y + -2) + 11 = 14y + -17

Reorder the terms:
14y(-2 + y) + 11 = 14y + -17
(-2 * 14y + y * 14y) + 11 = 14y + -17
(-28y + 14y2) + 11 = 14y + -17

Reorder the terms:
11 + -28y + 14y2 = 14y + -17

Reorder the terms:
11 + -28y + 14y2 = -17 + 14y

Solving
11 + -28y + 14y2 = -17 + 14y

Solving for variable 'y'.

Reorder the terms:
11 + 17 + -28y + -14y + 14y2 = -17 + 14y + 17 + -14y

Combine like terms: 11 + 17 = 28
28 + -28y + -14y + 14y2 = -17 + 14y + 17 + -14y

Combine like terms: -28y + -14y = -42y
28 + -42y + 14y2 = -17 + 14y + 17 + -14y

Reorder the terms:
28 + -42y + 14y2 = -17 + 17 + 14y + -14y

Combine like terms: -17 + 17 = 0
28 + -42y + 14y2 = 0 + 14y + -14y
28 + -42y + 14y2 = 14y + -14y

Combine like terms: 14y + -14y = 0
28 + -42y + 14y2 = 0

Factor out the Greatest Common Factor (GCF), '14'.
14(2 + -3y + y2) = 0

Factor a trinomial.
14((1 + -1y)(2 + -1y)) = 0

Ignore the factor 14.

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {1, 2}

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