-19y(y+2)+6(4y-6)=4(y-4)+12

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Solution for -19y(y+2)+6(4y-6)=4(y-4)+12 equation:


Simplifying
-19y(y + 2) + 6(4y + -6) = 4(y + -4) + 12

Reorder the terms:
-19y(2 + y) + 6(4y + -6) = 4(y + -4) + 12
(2 * -19y + y * -19y) + 6(4y + -6) = 4(y + -4) + 12
(-38y + -19y2) + 6(4y + -6) = 4(y + -4) + 12

Reorder the terms:
-38y + -19y2 + 6(-6 + 4y) = 4(y + -4) + 12
-38y + -19y2 + (-6 * 6 + 4y * 6) = 4(y + -4) + 12
-38y + -19y2 + (-36 + 24y) = 4(y + -4) + 12

Reorder the terms:
-36 + -38y + 24y + -19y2 = 4(y + -4) + 12

Combine like terms: -38y + 24y = -14y
-36 + -14y + -19y2 = 4(y + -4) + 12

Reorder the terms:
-36 + -14y + -19y2 = 4(-4 + y) + 12
-36 + -14y + -19y2 = (-4 * 4 + y * 4) + 12
-36 + -14y + -19y2 = (-16 + 4y) + 12

Reorder the terms:
-36 + -14y + -19y2 = -16 + 12 + 4y

Combine like terms: -16 + 12 = -4
-36 + -14y + -19y2 = -4 + 4y

Solving
-36 + -14y + -19y2 = -4 + 4y

Solving for variable 'y'.

Reorder the terms:
-36 + 4 + -14y + -4y + -19y2 = -4 + 4y + 4 + -4y

Combine like terms: -36 + 4 = -32
-32 + -14y + -4y + -19y2 = -4 + 4y + 4 + -4y

Combine like terms: -14y + -4y = -18y
-32 + -18y + -19y2 = -4 + 4y + 4 + -4y

Reorder the terms:
-32 + -18y + -19y2 = -4 + 4 + 4y + -4y

Combine like terms: -4 + 4 = 0
-32 + -18y + -19y2 = 0 + 4y + -4y
-32 + -18y + -19y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-32 + -18y + -19y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(32 + 18y + 19y2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(32 + 18y + 19y2)' equal to zero and attempt to solve: Simplifying 32 + 18y + 19y2 = 0 Solving 32 + 18y + 19y2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 1.684210526 + 0.9473684211y + y2 = 0 Move the constant term to the right: Add '-1.684210526' to each side of the equation. 1.684210526 + 0.9473684211y + -1.684210526 + y2 = 0 + -1.684210526 Reorder the terms: 1.684210526 + -1.684210526 + 0.9473684211y + y2 = 0 + -1.684210526 Combine like terms: 1.684210526 + -1.684210526 = 0.000000000 0.000000000 + 0.9473684211y + y2 = 0 + -1.684210526 0.9473684211y + y2 = 0 + -1.684210526 Combine like terms: 0 + -1.684210526 = -1.684210526 0.9473684211y + y2 = -1.684210526 The y term is 0.9473684211y. Take half its coefficient (0.4736842106). Square it (0.2243767314) and add it to both sides. Add '0.2243767314' to each side of the equation. 0.9473684211y + 0.2243767314 + y2 = -1.684210526 + 0.2243767314 Reorder the terms: 0.2243767314 + 0.9473684211y + y2 = -1.684210526 + 0.2243767314 Combine like terms: -1.684210526 + 0.2243767314 = -1.4598337946 0.2243767314 + 0.9473684211y + y2 = -1.4598337946 Factor a perfect square on the left side: (y + 0.4736842106)(y + 0.4736842106) = -1.4598337946 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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