4y(y+9)=7(y+9)

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Solution for 4y(y+9)=7(y+9) equation: 


Simplifying
4y(y + 9) = 7(y + 9)

Reorder the terms:
4y(9 + y) = 7(y + 9)
(9 * 4y + y * 4y) = 7(y + 9)
(36y + 4y2) = 7(y + 9)

Reorder the terms:
36y + 4y2 = 7(9 + y)
36y + 4y2 = (9 * 7 + y * 7)
36y + 4y2 = (63 + 7y)

Solving
36y + 4y2 = 63 + 7y

Solving for variable 'y'.

Reorder the terms:
-63 + 36y + -7y + 4y2 = 63 + 7y + -63 + -7y

Combine like terms: 36y + -7y = 29y
-63 + 29y + 4y2 = 63 + 7y + -63 + -7y

Reorder the terms:
-63 + 29y + 4y2 = 63 + -63 + 7y + -7y

Combine like terms: 63 + -63 = 0
-63 + 29y + 4y2 = 0 + 7y + -7y
-63 + 29y + 4y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-63 + 29y + 4y2 = 0

Factor a trinomial.
(-9 + -1y)(7 + -4y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -4y)' equal to zero and attempt to solve:

Simplifying
7 + -4y = 0

Solving
7 + -4y = 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 + -4y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4y = 0 + -7
-4y = 0 + -7

Combine like terms: 0 + -7 = -7
-4y = -7

Divide each side by '-4'.
y = 1.75

Simplifying
y = 1.75
Solution
y = {-9, 1.75}

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