2Y(4Y-3)=8(2)-18

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Solution for 2Y(4Y-3)=8(2)-18 equation: 


Simplifying
2Y(4Y + -3) = 8(2) + -18

Reorder the terms:
2Y(-3 + 4Y) = 8(2) + -18
(-3 * 2Y + 4Y * 2Y) = 8(2) + -18
(-6Y + 8Y2) = 8(2) + -18

Multiply 8 * 2
-6Y + 8Y2 = 16 + -18

Combine like terms: 16 + -18 = -2
-6Y + 8Y2 = -2

Solving
-6Y + 8Y2 = -2

Solving for variable 'Y'.

Reorder the terms:
2 + -6Y + 8Y2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -6Y + 8Y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -3Y + 4Y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -3Y + 4Y2)' equal to zero and attempt to solve:

Simplifying
1 + -3Y + 4Y2 = 0

Solving
1 + -3Y + 4Y2 = 0

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

Divide each side by '4'.
0.25 + -0.75Y + Y2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.75Y + -0.25 + Y2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.75Y + Y2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.75Y + Y2 = 0 + -0.25
-0.75Y + Y2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.75Y + Y2 = -0.25

The Y term is -0.75Y.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75Y + 0.140625 + Y2 = -0.25 + 0.140625

Reorder the terms:
0.140625 + -0.75Y + Y2 = -0.25 + 0.140625

Combine like terms: -0.25 + 0.140625 = -0.109375
0.140625 + -0.75Y + Y2 = -0.109375

Factor a perfect square on the left side:
(Y + -0.375)(Y + -0.375) = -0.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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