(5y+3)(y+4)=4(2y+3)

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


Simplifying
(5y + 3)(y + 4) = 4(2y + 3)

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

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

Multiply (3 + 5y) * (4 + y)
(3(4 + y) + 5y * (4 + y)) = 4(2y + 3)
((4 * 3 + y * 3) + 5y * (4 + y)) = 4(2y + 3)
((12 + 3y) + 5y * (4 + y)) = 4(2y + 3)
(12 + 3y + (4 * 5y + y * 5y)) = 4(2y + 3)
(12 + 3y + (20y + 5y2)) = 4(2y + 3)

Combine like terms: 3y + 20y = 23y
(12 + 23y + 5y2) = 4(2y + 3)

Reorder the terms:
12 + 23y + 5y2 = 4(3 + 2y)
12 + 23y + 5y2 = (3 * 4 + 2y * 4)
12 + 23y + 5y2 = (12 + 8y)

Add '-12' to each side of the equation.
12 + 23y + -12 + 5y2 = 12 + -12 + 8y

Reorder the terms:
12 + -12 + 23y + 5y2 = 12 + -12 + 8y

Combine like terms: 12 + -12 = 0
0 + 23y + 5y2 = 12 + -12 + 8y
23y + 5y2 = 12 + -12 + 8y

Combine like terms: 12 + -12 = 0
23y + 5y2 = 0 + 8y
23y + 5y2 = 8y

Solving
23y + 5y2 = 8y

Solving for variable 'y'.

Reorder the terms:
23y + -8y + 5y2 = 8y + -8y

Combine like terms: 23y + -8y = 15y
15y + 5y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
15y + 5y2 = 0

Factor out the Greatest Common Factor (GCF), '5y'.
5y(3 + y) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

Simplifying
y = -3
Solution
y = {0, -3}

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