(y-2)(3y+7)=0

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Solution for (y-2)(3y+7)=0 equation: 


Simplifying
(y + -2)(3y + 7) = 0

Reorder the terms:
(-2 + y)(3y + 7) = 0

Reorder the terms:
(-2 + y)(7 + 3y) = 0

Multiply (-2 + y) * (7 + 3y)
(-2(7 + 3y) + y(7 + 3y)) = 0
((7 * -2 + 3y * -2) + y(7 + 3y)) = 0
((-14 + -6y) + y(7 + 3y)) = 0
(-14 + -6y + (7 * y + 3y * y)) = 0
(-14 + -6y + (7y + 3y2)) = 0

Combine like terms: -6y + 7y = 1y
(-14 + 1y + 3y2) = 0

Solving
-14 + 1y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -3y)(2 + -1y) = 0


Subproblem 1
Set the factor '(-7 + -3y)' equal to zero and attempt to solve:

Simplifying
-7 + -3y = 0

Solving
-7 + -3y = 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 + -3y = 0 + 7

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

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

Divide each side by '-3'.
y = -2.333333333

Simplifying
y = -2.333333333

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-2.333333333, 2}

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