(y-2)*(2y+3)-2*(3y-2)*(y-2)=0

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Solution for (y-2)*(2y+3)-2*(3y-2)*(y-2)=0 equation: 


Simplifying
(y + -2)(2y + 3) + -2(3y + -2)(y + -2) = 0

Reorder the terms:
(-2 + y)(2y + 3) + -2(3y + -2)(y + -2) = 0

Reorder the terms:
(-2 + y)(3 + 2y) + -2(3y + -2)(y + -2) = 0

Multiply (-2 + y) * (3 + 2y)
(-2(3 + 2y) + y(3 + 2y)) + -2(3y + -2)(y + -2) = 0
((3 * -2 + 2y * -2) + y(3 + 2y)) + -2(3y + -2)(y + -2) = 0
((-6 + -4y) + y(3 + 2y)) + -2(3y + -2)(y + -2) = 0
(-6 + -4y + (3 * y + 2y * y)) + -2(3y + -2)(y + -2) = 0
(-6 + -4y + (3y + 2y2)) + -2(3y + -2)(y + -2) = 0

Combine like terms: -4y + 3y = -1y
(-6 + -1y + 2y2) + -2(3y + -2)(y + -2) = 0

Reorder the terms:
-6 + -1y + 2y2 + -2(-2 + 3y)(y + -2) = 0

Reorder the terms:
-6 + -1y + 2y2 + -2(-2 + 3y)(-2 + y) = 0

Multiply (-2 + 3y) * (-2 + y)
-6 + -1y + 2y2 + -2(-2(-2 + y) + 3y * (-2 + y)) = 0
-6 + -1y + 2y2 + -2((-2 * -2 + y * -2) + 3y * (-2 + y)) = 0
-6 + -1y + 2y2 + -2((4 + -2y) + 3y * (-2 + y)) = 0
-6 + -1y + 2y2 + -2(4 + -2y + (-2 * 3y + y * 3y)) = 0
-6 + -1y + 2y2 + -2(4 + -2y + (-6y + 3y2)) = 0

Combine like terms: -2y + -6y = -8y
-6 + -1y + 2y2 + -2(4 + -8y + 3y2) = 0
-6 + -1y + 2y2 + (4 * -2 + -8y * -2 + 3y2 * -2) = 0
-6 + -1y + 2y2 + (-8 + 16y + -6y2) = 0

Reorder the terms:
-6 + -8 + -1y + 16y + 2y2 + -6y2 = 0

Combine like terms: -6 + -8 = -14
-14 + -1y + 16y + 2y2 + -6y2 = 0

Combine like terms: -1y + 16y = 15y
-14 + 15y + 2y2 + -6y2 = 0

Combine like terms: 2y2 + -6y2 = -4y2
-14 + 15y + -4y2 = 0

Solving
-14 + 15y + -4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + y)(7 + -4y) = 0


Subproblem 1
Set the factor '(-2 + y)' equal to zero and attempt to solve:

Simplifying
-2 + y = 0

Solving
-2 + y = 0

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

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

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

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

Simplifying
y = 2

Subproblem 2
Set the factor '(7 + -4y)' equal to zero and attempt to solve:

Simplifying
7 + -4y = 0

Solving
7 + -4y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4y = 0 + -7
-4y = 0 + -7

Combine like terms: 0 + -7 = -7
-4y = -7

Divide each side by '-4'.
y = 1.75

Simplifying
y = 1.75
Solution
y = {2, 1.75}

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