-3Y(2Y+7)=-18

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Solution for -3Y(2Y+7)=-18 equation: 


Simplifying
-3Y(2Y + 7) = -18

Reorder the terms:
-3Y(7 + 2Y) = -18
(7 * -3Y + 2Y * -3Y) = -18
(-21Y + -6Y2) = -18

Solving
-21Y + -6Y2 = -18

Solving for variable 'Y'.

Reorder the terms:
18 + -21Y + -6Y2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + -21Y + -6Y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -7Y + -2Y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(6 + -7Y + -2Y2)' equal to zero and attempt to solve:

Simplifying
6 + -7Y + -2Y2 = 0

Solving
6 + -7Y + -2Y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3 + 3.5Y + Y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3.5Y + 3 + Y2 = 0 + 3

Reorder the terms:
-3 + 3 + 3.5Y + Y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3.5Y + Y2 = 0 + 3
3.5Y + Y2 = 0 + 3

Combine like terms: 0 + 3 = 3
3.5Y + Y2 = 3

The Y term is 3.5Y.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5Y + 3.0625 + Y2 = 3 + 3.0625

Reorder the terms:
3.0625 + 3.5Y + Y2 = 3 + 3.0625

Combine like terms: 3 + 3.0625 = 6.0625
3.0625 + 3.5Y + Y2 = 6.0625

Factor a perfect square on the left side:
(Y + 1.75)(Y + 1.75) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(Y + 1.75) equal to 2.46221445 and -2.46221445.


Subproblem 1
Y + 1.75 = 2.46221445

Simplifying
Y + 1.75 = 2.46221445

Reorder the terms:
1.75 + Y = 2.46221445

Solving
1.75 + Y = 2.46221445

Solving for variable 'Y'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + Y = 2.46221445 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + Y = 2.46221445 + -1.75
Y = 2.46221445 + -1.75

Combine like terms: 2.46221445 + -1.75 = 0.71221445
Y = 0.71221445

Simplifying
Y = 0.71221445


Subproblem 2
Y + 1.75 = -2.46221445

Simplifying
Y + 1.75 = -2.46221445

Reorder the terms:
1.75 + Y = -2.46221445

Solving
1.75 + Y = -2.46221445

Solving for variable 'Y'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + Y = -2.46221445 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + Y = -2.46221445 + -1.75
Y = -2.46221445 + -1.75

Combine like terms: -2.46221445 + -1.75 = -4.21221445
Y = -4.21221445

Simplifying
Y = -4.21221445


Solution
The solution to the problem is based on the solutions
from the subproblems.
Y = {0.71221445, -4.21221445}
Solution
Y = {0.71221445, -4.21221445}

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