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

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Solution for 7-7y=(3y+2y)(y-1) equation: 


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

Combine like terms: 3y + 2y = 5y
7 + -7y = (5y)(y + -1)

Remove parenthesis around (5y)
7 + -7y = 5y(y + -1)

Reorder the terms:
7 + -7y = 5y(-1 + y)
7 + -7y = (-1 * 5y + y * 5y)
7 + -7y = (-5y + 5y2)

Solving
7 + -7y = -5y + 5y2

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(1 + -1y)(7 + 5y) = 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 + 5y)' equal to zero and attempt to solve:

Simplifying
7 + 5y = 0

Solving
7 + 5y = 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 + 5y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5y = 0 + -7
5y = 0 + -7

Combine like terms: 0 + -7 = -7
5y = -7

Divide each side by '5'.
y = -1.4

Simplifying
y = -1.4
Solution
y = {1, -1.4}

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