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

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


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

Reorder the terms:
4y(7 + y) = 7(y + 7)
(7 * 4y + y * 4y) = 7(y + 7)
(28y + 4y2) = 7(y + 7)

Reorder the terms:
28y + 4y2 = 7(7 + y)
28y + 4y2 = (7 * 7 + y * 7)
28y + 4y2 = (49 + 7y)

Solving
28y + 4y2 = 49 + 7y

Solving for variable 'y'.

Reorder the terms:
-49 + 28y + -7y + 4y2 = 49 + 7y + -49 + -7y

Combine like terms: 28y + -7y = 21y
-49 + 21y + 4y2 = 49 + 7y + -49 + -7y

Reorder the terms:
-49 + 21y + 4y2 = 49 + -49 + 7y + -7y

Combine like terms: 49 + -49 = 0
-49 + 21y + 4y2 = 0 + 7y + -7y
-49 + 21y + 4y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-49 + 21y + 4y2 = 0

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


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

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 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 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7

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 = {-7, 1.75}

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