(3y)(2y+7)=(6)(11)

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Solution for (3y)(2y+7)=(6)(11) equation: 


Simplifying
(3y)(2y + 7) = (6)(11)

Remove parenthesis around (3y)
3y(2y + 7) = (6)(11)

Reorder the terms:
3y(7 + 2y) = (6)(11)
(7 * 3y + 2y * 3y) = (6)(11)
(21y + 6y2) = (6)(11)

Multiply 6 * 11
21y + 6y2 = 66

Solving
21y + 6y2 = 66

Solving for variable 'y'.

Reorder the terms:
-66 + 21y + 6y2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + 21y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + 7y + 2y2) = 0

Factor a trinomial.
3((-11 + -2y)(2 + -1y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + -2y)' equal to zero and attempt to solve:

Simplifying
-11 + -2y = 0

Solving
-11 + -2y = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2y = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2y = 0 + 11
-2y = 0 + 11

Combine like terms: 0 + 11 = 11
-2y = 11

Divide each side by '-2'.
y = -5.5

Simplifying
y = -5.5

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 = {-5.5, 2}

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