(-2y+3)(6y-1)=4(5y-6)

Solution for (-2y+3)(6y-1)=4(5y-6) equation:

Simplifying
(-2y + 3)(6y + -1) = 4(5y + -6)

Reorder the terms:
(3 + -2y)(6y + -1) = 4(5y + -6)

Reorder the terms:
(3 + -2y)(-1 + 6y) = 4(5y + -6)

Multiply (3 + -2y) * (-1 + 6y)
(3(-1 + 6y) + -2y * (-1 + 6y)) = 4(5y + -6)
((-1 * 3 + 6y * 3) + -2y * (-1 + 6y)) = 4(5y + -6)
((-3 + 18y) + -2y * (-1 + 6y)) = 4(5y + -6)
(-3 + 18y + (-1 * -2y + 6y * -2y)) = 4(5y + -6)
(-3 + 18y + (2y + -12y2)) = 4(5y + -6)

Combine like terms: 18y + 2y = 20y
(-3 + 20y + -12y2) = 4(5y + -6)

Reorder the terms:
-3 + 20y + -12y2 = 4(-6 + 5y)
-3 + 20y + -12y2 = (-6 * 4 + 5y * 4)
-3 + 20y + -12y2 = (-24 + 20y)

Add '-20y' to each side of the equation.
-3 + 20y + -20y + -12y2 = -24 + 20y + -20y

Combine like terms: 20y + -20y = 0
-3 + 0 + -12y2 = -24 + 20y + -20y
-3 + -12y2 = -24 + 20y + -20y

Combine like terms: 20y + -20y = 0
-3 + -12y2 = -24 + 0
-3 + -12y2 = -24

Solving
-3 + -12y2 = -24

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + -12y2 = -24 + 3

Combine like terms: -3 + 3 = 0
0 + -12y2 = -24 + 3
-12y2 = -24 + 3

Combine like terms: -24 + 3 = -21
-12y2 = -21

Divide each side by '-12'.
y2 = 1.75

Simplifying
y2 = 1.75

Take the square root of each side:
y = {-1.322875656, 1.322875656}