-3y(4y-5)-y=-4(y-5)

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Solution for -3y(4y-5)-y=-4(y-5) equation:


Simplifying
-3y(4y + -5) + -1y = -4(y + -5)

Reorder the terms:
-3y(-5 + 4y) + -1y = -4(y + -5)
(-5 * -3y + 4y * -3y) + -1y = -4(y + -5)
(15y + -12y2) + -1y = -4(y + -5)

Reorder the terms:
15y + -1y + -12y2 = -4(y + -5)

Combine like terms: 15y + -1y = 14y
14y + -12y2 = -4(y + -5)

Reorder the terms:
14y + -12y2 = -4(-5 + y)
14y + -12y2 = (-5 * -4 + y * -4)
14y + -12y2 = (20 + -4y)

Solving
14y + -12y2 = 20 + -4y

Solving for variable 'y'.

Reorder the terms:
-20 + 14y + 4y + -12y2 = 20 + -4y + -20 + 4y

Combine like terms: 14y + 4y = 18y
-20 + 18y + -12y2 = 20 + -4y + -20 + 4y

Reorder the terms:
-20 + 18y + -12y2 = 20 + -20 + -4y + 4y

Combine like terms: 20 + -20 = 0
-20 + 18y + -12y2 = 0 + -4y + 4y
-20 + 18y + -12y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
-20 + 18y + -12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 9y + -6y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-10 + 9y + -6y2)' equal to zero and attempt to solve: Simplifying -10 + 9y + -6y2 = 0 Solving -10 + 9y + -6y2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 1.666666667 + -1.5y + y2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.5y + -1.666666667 + y2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.5y + y2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.5y + y2 = 0 + -1.666666667 -1.5y + y2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.5y + y2 = -1.666666667 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = -1.666666667 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = -1.666666667 + 0.5625 Combine like terms: -1.666666667 + 0.5625 = -1.104166667 0.5625 + -1.5y + y2 = -1.104166667 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = -1.104166667 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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