10y(2y-5)-5(2y-5)=

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Solution for 10y(2y-5)-5(2y-5)= equation: 


Simplifying
10y(2y + -5) + -5(2y + -5) = 0

Reorder the terms:
10y(-5 + 2y) + -5(2y + -5) = 0
(-5 * 10y + 2y * 10y) + -5(2y + -5) = 0
(-50y + 20y2) + -5(2y + -5) = 0

Reorder the terms:
-50y + 20y2 + -5(-5 + 2y) = 0
-50y + 20y2 + (-5 * -5 + 2y * -5) = 0
-50y + 20y2 + (25 + -10y) = 0

Reorder the terms:
25 + -50y + -10y + 20y2 = 0

Combine like terms: -50y + -10y = -60y
25 + -60y + 20y2 = 0

Solving
25 + -60y + 20y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -12y + 4y2) = 0

Factor a trinomial.
5((1 + -2y)(5 + -2y)) = 0

Ignore the factor 5.

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

Simplifying
1 + -2y = 0

Solving
1 + -2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5

Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 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 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {0.5, 2.5}

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