y(y-12)=5(7-2y)

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Solution for y(y-12)=5(7-2y) equation: 


Simplifying
y(y + -12) = 5(7 + -2y)

Reorder the terms:
y(-12 + y) = 5(7 + -2y)
(-12 * y + y * y) = 5(7 + -2y)
(-12y + y2) = 5(7 + -2y)
-12y + y2 = (7 * 5 + -2y * 5)
-12y + y2 = (35 + -10y)

Solving
-12y + y2 = 35 + -10y

Solving for variable 'y'.

Reorder the terms:
-35 + -12y + 10y + y2 = 35 + -10y + -35 + 10y

Combine like terms: -12y + 10y = -2y
-35 + -2y + y2 = 35 + -10y + -35 + 10y

Reorder the terms:
-35 + -2y + y2 = 35 + -35 + -10y + 10y

Combine like terms: 35 + -35 = 0
-35 + -2y + y2 = 0 + -10y + 10y
-35 + -2y + y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
-35 + -2y + y2 = 0

Factor a trinomial.
(-5 + -1y)(7 + -1y) = 0


Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5

Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-5, 7}

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