1y(1y+12)-8y=14+y(y-4)

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Solution for 1y(1y+12)-8y=14+y(y-4) equation: 


Simplifying
1y(1y + 12) + -8y = 14 + y(y + -4)

Reorder the terms:
1y(12 + 1y) + -8y = 14 + y(y + -4)
(12 * 1y + 1y * 1y) + -8y = 14 + y(y + -4)
(12y + 1y2) + -8y = 14 + y(y + -4)

Reorder the terms:
12y + -8y + 1y2 = 14 + y(y + -4)

Combine like terms: 12y + -8y = 4y
4y + 1y2 = 14 + y(y + -4)

Reorder the terms:
4y + 1y2 = 14 + y(-4 + y)
4y + 1y2 = 14 + (-4 * y + y * y)
4y + 1y2 = 14 + (-4y + y2)

Solving
4y + 1y2 = 14 + -4y + y2

Solving for variable 'y'.

Reorder the terms:
-14 + 4y + 4y + 1y2 + -1y2 = 14 + -4y + y2 + -14 + 4y + -1y2

Combine like terms: 4y + 4y = 8y
-14 + 8y + 1y2 + -1y2 = 14 + -4y + y2 + -14 + 4y + -1y2

Combine like terms: 1y2 + -1y2 = 0
-14 + 8y + 0 = 14 + -4y + y2 + -14 + 4y + -1y2
-14 + 8y = 14 + -4y + y2 + -14 + 4y + -1y2

Reorder the terms:
-14 + 8y = 14 + -14 + -4y + 4y + y2 + -1y2

Combine like terms: 14 + -14 = 0
-14 + 8y = 0 + -4y + 4y + y2 + -1y2
-14 + 8y = -4y + 4y + y2 + -1y2

Combine like terms: -4y + 4y = 0
-14 + 8y = 0 + y2 + -1y2
-14 + 8y = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-14 + 8y = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 4y) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 4y)' equal to zero and attempt to solve:

Simplifying
-7 + 4y = 0

Solving
-7 + 4y = 0

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

Add '7' to each side of the equation.
-7 + 7 + 4y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4y = 0 + 7
4y = 0 + 7

Combine like terms: 0 + 7 = 7
4y = 7

Divide each side by '4'.
y = 1.75

Simplifying
y = 1.75
Solution
y = {1.75}

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