2+4y(y-3)=4y-10

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Solution for 2+4y(y-3)=4y-10 equation: 


Simplifying
2 + 4y(y + -3) = 4y + -10

Reorder the terms:
2 + 4y(-3 + y) = 4y + -10
2 + (-3 * 4y + y * 4y) = 4y + -10
2 + (-12y + 4y2) = 4y + -10

Reorder the terms:
2 + -12y + 4y2 = -10 + 4y

Solving
2 + -12y + 4y2 = -10 + 4y

Solving for variable 'y'.

Reorder the terms:
2 + 10 + -12y + -4y + 4y2 = -10 + 4y + 10 + -4y

Combine like terms: 2 + 10 = 12
12 + -12y + -4y + 4y2 = -10 + 4y + 10 + -4y

Combine like terms: -12y + -4y = -16y
12 + -16y + 4y2 = -10 + 4y + 10 + -4y

Reorder the terms:
12 + -16y + 4y2 = -10 + 10 + 4y + -4y

Combine like terms: -10 + 10 = 0
12 + -16y + 4y2 = 0 + 4y + -4y
12 + -16y + 4y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
12 + -16y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -4y + y2) = 0

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

Ignore the factor 4.

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1

Subproblem 2
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
Solution
y = {1, 3}

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