4y(y+5)=7(y+5)

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Solution for 4y(y+5)=7(y+5) equation: 


Simplifying
4y(y + 5) = 7(y + 5)

Reorder the terms:
4y(5 + y) = 7(y + 5)
(5 * 4y + y * 4y) = 7(y + 5)
(20y + 4y2) = 7(y + 5)

Reorder the terms:
20y + 4y2 = 7(5 + y)
20y + 4y2 = (5 * 7 + y * 7)
20y + 4y2 = (35 + 7y)

Solving
20y + 4y2 = 35 + 7y

Solving for variable 'y'.

Reorder the terms:
-35 + 20y + -7y + 4y2 = 35 + 7y + -35 + -7y

Combine like terms: 20y + -7y = 13y
-35 + 13y + 4y2 = 35 + 7y + -35 + -7y

Reorder the terms:
-35 + 13y + 4y2 = 35 + -35 + 7y + -7y

Combine like terms: 35 + -35 = 0
-35 + 13y + 4y2 = 0 + 7y + -7y
-35 + 13y + 4y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-35 + 13y + 4y2 = 0

Factor a trinomial.
(-5 + -1y)(7 + -4y) = 0


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

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5

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 = {-5, 1.75}

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