y(2y+7)=9(2y+7)

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Solution for y(2y+7)=9(2y+7) equation: 


Simplifying
y(2y + 7) = 9(2y + 7)

Reorder the terms:
y(7 + 2y) = 9(2y + 7)
(7 * y + 2y * y) = 9(2y + 7)
(7y + 2y2) = 9(2y + 7)

Reorder the terms:
7y + 2y2 = 9(7 + 2y)
7y + 2y2 = (7 * 9 + 2y * 9)
7y + 2y2 = (63 + 18y)

Solving
7y + 2y2 = 63 + 18y

Solving for variable 'y'.

Reorder the terms:
-63 + 7y + -18y + 2y2 = 63 + 18y + -63 + -18y

Combine like terms: 7y + -18y = -11y
-63 + -11y + 2y2 = 63 + 18y + -63 + -18y

Reorder the terms:
-63 + -11y + 2y2 = 63 + -63 + 18y + -18y

Combine like terms: 63 + -63 = 0
-63 + -11y + 2y2 = 0 + 18y + -18y
-63 + -11y + 2y2 = 18y + -18y

Combine like terms: 18y + -18y = 0
-63 + -11y + 2y2 = 0

Factor a trinomial.
(-7 + -2y)(9 + -1y) = 0


Subproblem 1
Set the factor '(-7 + -2y)' equal to zero and attempt to solve:

Simplifying
-7 + -2y = 0

Solving
-7 + -2y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2y = 0 + 7
-2y = 0 + 7

Combine like terms: 0 + 7 = 7
-2y = 7

Divide each side by '-2'.
y = -3.5

Simplifying
y = -3.5

Subproblem 2
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {-3.5, 9}

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