(5y+3)(2y-6)+20=-6

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Solution for (5y+3)(2y-6)+20=-6 equation: 


Simplifying
(5y + 3)(2y + -6) + 20 = -6

Reorder the terms:
(3 + 5y)(2y + -6) + 20 = -6

Reorder the terms:
(3 + 5y)(-6 + 2y) + 20 = -6

Multiply (3 + 5y) * (-6 + 2y)
(3(-6 + 2y) + 5y * (-6 + 2y)) + 20 = -6
((-6 * 3 + 2y * 3) + 5y * (-6 + 2y)) + 20 = -6
((-18 + 6y) + 5y * (-6 + 2y)) + 20 = -6
(-18 + 6y + (-6 * 5y + 2y * 5y)) + 20 = -6
(-18 + 6y + (-30y + 10y2)) + 20 = -6

Combine like terms: 6y + -30y = -24y
(-18 + -24y + 10y2) + 20 = -6

Reorder the terms:
-18 + 20 + -24y + 10y2 = -6

Combine like terms: -18 + 20 = 2
2 + -24y + 10y2 = -6

Solving
2 + -24y + 10y2 = -6

Solving for variable 'y'.

Reorder the terms:
2 + 6 + -24y + 10y2 = -6 + 6

Combine like terms: 2 + 6 = 8
8 + -24y + 10y2 = -6 + 6

Combine like terms: -6 + 6 = 0
8 + -24y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -12y + 5y2) = 0

Factor a trinomial.
2((2 + -5y)(2 + -1y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -5y)' equal to zero and attempt to solve:

Simplifying
2 + -5y = 0

Solving
2 + -5y = 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 + -5y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y = 0 + -2
-5y = 0 + -2

Combine like terms: 0 + -2 = -2
-5y = -2

Divide each side by '-5'.
y = 0.4

Simplifying
y = 0.4

Subproblem 2
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
Solution
y = {0.4, 2}

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