(2y+1)(3y-2)-(6y-1)(y+4)=-20y

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Solution for (2y+1)(3y-2)-(6y-1)(y+4)=-20y equation: 


Simplifying
(2y + 1)(3y + -2) + -1(6y + -1)(y + 4) = -20y

Reorder the terms:
(1 + 2y)(3y + -2) + -1(6y + -1)(y + 4) = -20y

Reorder the terms:
(1 + 2y)(-2 + 3y) + -1(6y + -1)(y + 4) = -20y

Multiply (1 + 2y) * (-2 + 3y)
(1(-2 + 3y) + 2y * (-2 + 3y)) + -1(6y + -1)(y + 4) = -20y
((-2 * 1 + 3y * 1) + 2y * (-2 + 3y)) + -1(6y + -1)(y + 4) = -20y
((-2 + 3y) + 2y * (-2 + 3y)) + -1(6y + -1)(y + 4) = -20y
(-2 + 3y + (-2 * 2y + 3y * 2y)) + -1(6y + -1)(y + 4) = -20y
(-2 + 3y + (-4y + 6y2)) + -1(6y + -1)(y + 4) = -20y

Combine like terms: 3y + -4y = -1y
(-2 + -1y + 6y2) + -1(6y + -1)(y + 4) = -20y

Reorder the terms:
-2 + -1y + 6y2 + -1(-1 + 6y)(y + 4) = -20y

Reorder the terms:
-2 + -1y + 6y2 + -1(-1 + 6y)(4 + y) = -20y

Multiply (-1 + 6y) * (4 + y)
-2 + -1y + 6y2 + -1(-1(4 + y) + 6y * (4 + y)) = -20y
-2 + -1y + 6y2 + -1((4 * -1 + y * -1) + 6y * (4 + y)) = -20y
-2 + -1y + 6y2 + -1((-4 + -1y) + 6y * (4 + y)) = -20y
-2 + -1y + 6y2 + -1(-4 + -1y + (4 * 6y + y * 6y)) = -20y
-2 + -1y + 6y2 + -1(-4 + -1y + (24y + 6y2)) = -20y

Combine like terms: -1y + 24y = 23y
-2 + -1y + 6y2 + -1(-4 + 23y + 6y2) = -20y
-2 + -1y + 6y2 + (-4 * -1 + 23y * -1 + 6y2 * -1) = -20y
-2 + -1y + 6y2 + (4 + -23y + -6y2) = -20y

Reorder the terms:
-2 + 4 + -1y + -23y + 6y2 + -6y2 = -20y

Combine like terms: -2 + 4 = 2
2 + -1y + -23y + 6y2 + -6y2 = -20y

Combine like terms: -1y + -23y = -24y
2 + -24y + 6y2 + -6y2 = -20y

Combine like terms: 6y2 + -6y2 = 0
2 + -24y + 0 = -20y
2 + -24y = -20y

Solving
2 + -24y = -20y

Solving for variable 'y'.

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

Add '20y' to each side of the equation.
2 + -24y + 20y = -20y + 20y

Combine like terms: -24y + 20y = -4y
2 + -4y = -20y + 20y

Combine like terms: -20y + 20y = 0
2 + -4y = 0

Add '-2' to each side of the equation.
2 + -2 + -4y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4y = 0 + -2
-4y = 0 + -2

Combine like terms: 0 + -2 = -2
-4y = -2

Divide each side by '-4'.
y = 0.5

Simplifying
y = 0.5

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