2y(y-3)=7-y

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Solution for 2y(y-3)=7-y equation: 


Simplifying
2y(y + -3) = 7 + -1y

Reorder the terms:
2y(-3 + y) = 7 + -1y
(-3 * 2y + y * 2y) = 7 + -1y
(-6y + 2y2) = 7 + -1y

Solving
-6y + 2y2 = 7 + -1y

Solving for variable 'y'.

Reorder the terms:
-7 + -6y + y + 2y2 = 7 + -1y + -7 + y

Combine like terms: -6y + y = -5y
-7 + -5y + 2y2 = 7 + -1y + -7 + y

Reorder the terms:
-7 + -5y + 2y2 = 7 + -7 + -1y + y

Combine like terms: 7 + -7 = 0
-7 + -5y + 2y2 = 0 + -1y + y
-7 + -5y + 2y2 = -1y + y

Combine like terms: -1y + y = 0
-7 + -5y + 2y2 = 0

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


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 '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 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 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {-1, 3.5}

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