(y-2)(y+5)=7y-10

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Solution for (y-2)(y+5)=7y-10 equation: 


Simplifying
(y + -2)(y + 5) = 7y + -10

Reorder the terms:
(-2 + y)(y + 5) = 7y + -10

Reorder the terms:
(-2 + y)(5 + y) = 7y + -10

Multiply (-2 + y) * (5 + y)
(-2(5 + y) + y(5 + y)) = 7y + -10
((5 * -2 + y * -2) + y(5 + y)) = 7y + -10
((-10 + -2y) + y(5 + y)) = 7y + -10
(-10 + -2y + (5 * y + y * y)) = 7y + -10
(-10 + -2y + (5y + y2)) = 7y + -10

Combine like terms: -2y + 5y = 3y
(-10 + 3y + y2) = 7y + -10

Reorder the terms:
-10 + 3y + y2 = -10 + 7y

Add '10' to each side of the equation.
-10 + 3y + 10 + y2 = -10 + 10 + 7y

Reorder the terms:
-10 + 10 + 3y + y2 = -10 + 10 + 7y

Combine like terms: -10 + 10 = 0
0 + 3y + y2 = -10 + 10 + 7y
3y + y2 = -10 + 10 + 7y

Combine like terms: -10 + 10 = 0
3y + y2 = 0 + 7y
3y + y2 = 7y

Solving
3y + y2 = 7y

Solving for variable 'y'.

Reorder the terms:
3y + -7y + y2 = 7y + -7y

Combine like terms: 3y + -7y = -4y
-4y + y2 = 7y + -7y

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

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


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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

Simplifying
-4 + y = 0

Solving
-4 + y = 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 + y = 0 + 4

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

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

Simplifying
y = 4
Solution
y = {0, 4}

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