7y-6y(y-1)+3=12-9

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Solution for 7y-6y(y-1)+3=12-9 equation: 


Simplifying
7y + -6y(y + -1) + 3 = 12 + -9

Reorder the terms:
7y + -6y(-1 + y) + 3 = 12 + -9
7y + (-1 * -6y + y * -6y) + 3 = 12 + -9
7y + (6y + -6y2) + 3 = 12 + -9

Reorder the terms:
3 + 7y + 6y + -6y2 = 12 + -9

Combine like terms: 7y + 6y = 13y
3 + 13y + -6y2 = 12 + -9

Combine like terms: 12 + -9 = 3
3 + 13y + -6y2 = 3

Add '-3' to each side of the equation.
3 + 13y + -3 + -6y2 = 3 + -3

Reorder the terms:
3 + -3 + 13y + -6y2 = 3 + -3

Combine like terms: 3 + -3 = 0
0 + 13y + -6y2 = 3 + -3
13y + -6y2 = 3 + -3

Combine like terms: 3 + -3 = 0
13y + -6y2 = 0

Solving
13y + -6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(13 + -6y) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(13 + -6y)' equal to zero and attempt to solve:

Simplifying
13 + -6y = 0

Solving
13 + -6y = 0

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

Add '-13' to each side of the equation.
13 + -13 + -6y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -6y = 0 + -13
-6y = 0 + -13

Combine like terms: 0 + -13 = -13
-6y = -13

Divide each side by '-6'.
y = 2.166666667

Simplifying
y = 2.166666667
Solution
y = {0, 2.166666667}

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