(3y-2)(2y+1)=3y^2-11y-10

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Solution for (3y-2)(2y+1)=3y^2-11y-10 equation: 


Simplifying
(3y + -2)(2y + 1) = 3y2 + -11y + -10

Reorder the terms:
(-2 + 3y)(2y + 1) = 3y2 + -11y + -10

Reorder the terms:
(-2 + 3y)(1 + 2y) = 3y2 + -11y + -10

Multiply (-2 + 3y) * (1 + 2y)
(-2(1 + 2y) + 3y * (1 + 2y)) = 3y2 + -11y + -10
((1 * -2 + 2y * -2) + 3y * (1 + 2y)) = 3y2 + -11y + -10
((-2 + -4y) + 3y * (1 + 2y)) = 3y2 + -11y + -10
(-2 + -4y + (1 * 3y + 2y * 3y)) = 3y2 + -11y + -10
(-2 + -4y + (3y + 6y2)) = 3y2 + -11y + -10

Combine like terms: -4y + 3y = -1y
(-2 + -1y + 6y2) = 3y2 + -11y + -10

Reorder the terms:
-2 + -1y + 6y2 = -10 + -11y + 3y2

Solving
-2 + -1y + 6y2 = -10 + -11y + 3y2

Solving for variable 'y'.

Reorder the terms:
-2 + 10 + -1y + 11y + 6y2 + -3y2 = -10 + -11y + 3y2 + 10 + 11y + -3y2

Combine like terms: -2 + 10 = 8
8 + -1y + 11y + 6y2 + -3y2 = -10 + -11y + 3y2 + 10 + 11y + -3y2

Combine like terms: -1y + 11y = 10y
8 + 10y + 6y2 + -3y2 = -10 + -11y + 3y2 + 10 + 11y + -3y2

Combine like terms: 6y2 + -3y2 = 3y2
8 + 10y + 3y2 = -10 + -11y + 3y2 + 10 + 11y + -3y2

Reorder the terms:
8 + 10y + 3y2 = -10 + 10 + -11y + 11y + 3y2 + -3y2

Combine like terms: -10 + 10 = 0
8 + 10y + 3y2 = 0 + -11y + 11y + 3y2 + -3y2
8 + 10y + 3y2 = -11y + 11y + 3y2 + -3y2

Combine like terms: -11y + 11y = 0
8 + 10y + 3y2 = 0 + 3y2 + -3y2
8 + 10y + 3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
8 + 10y + 3y2 = 0

Factor a trinomial.
(2 + y)(4 + 3y) = 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 '(4 + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3y = 0

Solving
4 + 3y = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3y = 0 + -4
3y = 0 + -4

Combine like terms: 0 + -4 = -4
3y = -4

Divide each side by '3'.
y = -1.333333333

Simplifying
y = -1.333333333
Solution
y = {-2, -1.333333333}

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