2y(4y+3)=24+2y

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Solution for 2y(4y+3)=24+2y equation: 


Simplifying
2y(4y + 3) = 24 + 2y

Reorder the terms:
2y(3 + 4y) = 24 + 2y
(3 * 2y + 4y * 2y) = 24 + 2y
(6y + 8y2) = 24 + 2y

Solving
6y + 8y2 = 24 + 2y

Solving for variable 'y'.

Reorder the terms:
-24 + 6y + -2y + 8y2 = 24 + 2y + -24 + -2y

Combine like terms: 6y + -2y = 4y
-24 + 4y + 8y2 = 24 + 2y + -24 + -2y

Reorder the terms:
-24 + 4y + 8y2 = 24 + -24 + 2y + -2y

Combine like terms: 24 + -24 = 0
-24 + 4y + 8y2 = 0 + 2y + -2y
-24 + 4y + 8y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-24 + 4y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + y + 2y2) = 0

Factor a trinomial.
4((-2 + -1y)(3 + -2y)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2

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 = {-2, 1.5}

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