4y(2y-3)=-6y+9

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Solution for 4y(2y-3)=-6y+9 equation: 


Simplifying
4y(2y + -3) = -6y + 9

Reorder the terms:
4y(-3 + 2y) = -6y + 9
(-3 * 4y + 2y * 4y) = -6y + 9
(-12y + 8y2) = -6y + 9

Reorder the terms:
-12y + 8y2 = 9 + -6y

Solving
-12y + 8y2 = 9 + -6y

Solving for variable 'y'.

Reorder the terms:
-9 + -12y + 6y + 8y2 = 9 + -6y + -9 + 6y

Combine like terms: -12y + 6y = -6y
-9 + -6y + 8y2 = 9 + -6y + -9 + 6y

Reorder the terms:
-9 + -6y + 8y2 = 9 + -9 + -6y + 6y

Combine like terms: 9 + -9 = 0
-9 + -6y + 8y2 = 0 + -6y + 6y
-9 + -6y + 8y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-9 + -6y + 8y2 = 0

Factor a trinomial.
(-3 + -4y)(3 + -2y) = 0


Subproblem 1
Set the factor '(-3 + -4y)' equal to zero and attempt to solve:

Simplifying
-3 + -4y = 0

Solving
-3 + -4y = 0

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

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

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

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

Divide each side by '-4'.
y = -0.75

Simplifying
y = -0.75

Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-0.75, 1.5}

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