(2y+4)(y-3)=100

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Solution for (2y+4)(y-3)=100 equation: 


Simplifying
(2y + 4)(y + -3) = 100

Reorder the terms:
(4 + 2y)(y + -3) = 100

Reorder the terms:
(4 + 2y)(-3 + y) = 100

Multiply (4 + 2y) * (-3 + y)
(4(-3 + y) + 2y * (-3 + y)) = 100
((-3 * 4 + y * 4) + 2y * (-3 + y)) = 100
((-12 + 4y) + 2y * (-3 + y)) = 100
(-12 + 4y + (-3 * 2y + y * 2y)) = 100
(-12 + 4y + (-6y + 2y2)) = 100

Combine like terms: 4y + -6y = -2y
(-12 + -2y + 2y2) = 100

Solving
-12 + -2y + 2y2 = 100

Solving for variable 'y'.

Reorder the terms:
-12 + -100 + -2y + 2y2 = 100 + -100

Combine like terms: -12 + -100 = -112
-112 + -2y + 2y2 = 100 + -100

Combine like terms: 100 + -100 = 0
-112 + -2y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-56 + -1y + y2) = 0

Factor a trinomial.
2((-7 + -1y)(8 + -1y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 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 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7

Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {-7, 8}

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