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Simplifying
(5y2 + -3y + 2) + -1(3y2 + -3y + 5) = 0
Reorder the terms:
(2 + -3y + 5y2) + -1(3y2 + -3y + 5) = 0
Remove parenthesis around (2 + -3y + 5y2)
2 + -3y + 5y2 + -1(3y2 + -3y + 5) = 0
Reorder the terms:
2 + -3y + 5y2 + -1(5 + -3y + 3y2) = 0
2 + -3y + 5y2 + (5 * -1 + -3y * -1 + 3y2 * -1) = 0
2 + -3y + 5y2 + (-5 + 3y + -3y2) = 0
Reorder the terms:
2 + -5 + -3y + 3y + 5y2 + -3y2 = 0
Combine like terms: 2 + -5 = -3
-3 + -3y + 3y + 5y2 + -3y2 = 0
Combine like terms: -3y + 3y = 0
-3 + 0 + 5y2 + -3y2 = 0
-3 + 5y2 + -3y2 = 0
Combine like terms: 5y2 + -3y2 = 2y2
-3 + 2y2 = 0
Solving
-3 + 2y2 = 0
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '3' to each side of the equation.
-3 + 3 + 2y2 = 0 + 3
Combine like terms: -3 + 3 = 0
0 + 2y2 = 0 + 3
2y2 = 0 + 3
Combine like terms: 0 + 3 = 3
2y2 = 3
Divide each side by '2'.
y2 = 1.5
Simplifying
y2 = 1.5
Take the square root of each side:
y = {-1.224744871, 1.224744871}
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