y^2+(y-7)(y-7)=25

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Solution for y^2+(y-7)(y-7)=25 equation: 


Simplifying
y2 + (y + -7)(y + -7) = 25

Reorder the terms:
y2 + (-7 + y)(y + -7) = 25

Reorder the terms:
y2 + (-7 + y)(-7 + y) = 25

Multiply (-7 + y) * (-7 + y)
y2 + (-7(-7 + y) + y(-7 + y)) = 25
y2 + ((-7 * -7 + y * -7) + y(-7 + y)) = 25
y2 + ((49 + -7y) + y(-7 + y)) = 25
y2 + (49 + -7y + (-7 * y + y * y)) = 25
y2 + (49 + -7y + (-7y + y2)) = 25

Combine like terms: -7y + -7y = -14y
y2 + (49 + -14y + y2) = 25

Reorder the terms:
49 + -14y + y2 + y2 = 25

Combine like terms: y2 + y2 = 2y2
49 + -14y + 2y2 = 25

Solving
49 + -14y + 2y2 = 25

Solving for variable 'y'.

Reorder the terms:
49 + -25 + -14y + 2y2 = 25 + -25

Combine like terms: 49 + -25 = 24
24 + -14y + 2y2 = 25 + -25

Combine like terms: 25 + -25 = 0
24 + -14y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -7y + y2) = 0

Factor a trinomial.
2((3 + -1y)(4 + -1y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3

Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {3, 4}

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