10(5y+2)+4y=5y(5y+2)+8

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Solution for 10(5y+2)+4y=5y(5y+2)+8 equation: 


Simplifying
10(5y + 2) + 4y = 5y(5y + 2) + 8

Reorder the terms:
10(2 + 5y) + 4y = 5y(5y + 2) + 8
(2 * 10 + 5y * 10) + 4y = 5y(5y + 2) + 8
(20 + 50y) + 4y = 5y(5y + 2) + 8

Combine like terms: 50y + 4y = 54y
20 + 54y = 5y(5y + 2) + 8

Reorder the terms:
20 + 54y = 5y(2 + 5y) + 8
20 + 54y = (2 * 5y + 5y * 5y) + 8
20 + 54y = (10y + 25y2) + 8

Reorder the terms:
20 + 54y = 8 + 10y + 25y2

Solving
20 + 54y = 8 + 10y + 25y2

Solving for variable 'y'.

Reorder the terms:
20 + -8 + 54y + -10y + -25y2 = 8 + 10y + 25y2 + -8 + -10y + -25y2

Combine like terms: 20 + -8 = 12
12 + 54y + -10y + -25y2 = 8 + 10y + 25y2 + -8 + -10y + -25y2

Combine like terms: 54y + -10y = 44y
12 + 44y + -25y2 = 8 + 10y + 25y2 + -8 + -10y + -25y2

Reorder the terms:
12 + 44y + -25y2 = 8 + -8 + 10y + -10y + 25y2 + -25y2

Combine like terms: 8 + -8 = 0
12 + 44y + -25y2 = 0 + 10y + -10y + 25y2 + -25y2
12 + 44y + -25y2 = 10y + -10y + 25y2 + -25y2

Combine like terms: 10y + -10y = 0
12 + 44y + -25y2 = 0 + 25y2 + -25y2
12 + 44y + -25y2 = 25y2 + -25y2

Combine like terms: 25y2 + -25y2 = 0
12 + 44y + -25y2 = 0

Factor a trinomial.
(2 + -1y)(6 + 25y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + 25y)' equal to zero and attempt to solve:

Simplifying
6 + 25y = 0

Solving
6 + 25y = 0

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

Add '-6' to each side of the equation.
6 + -6 + 25y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 25y = 0 + -6
25y = 0 + -6

Combine like terms: 0 + -6 = -6
25y = -6

Divide each side by '25'.
y = -0.24

Simplifying
y = -0.24
Solution
y = {2, -0.24}

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