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Simplifying
(2y2 + -1y + 3) + -1(3y2 + -1y + -4) = 0
Reorder the terms:
(3 + -1y + 2y2) + -1(3y2 + -1y + -4) = 0
Remove parenthesis around (3 + -1y + 2y2)
3 + -1y + 2y2 + -1(3y2 + -1y + -4) = 0
Reorder the terms:
3 + -1y + 2y2 + -1(-4 + -1y + 3y2) = 0
3 + -1y + 2y2 + (-4 * -1 + -1y * -1 + 3y2 * -1) = 0
3 + -1y + 2y2 + (4 + 1y + -3y2) = 0
Reorder the terms:
3 + 4 + -1y + 1y + 2y2 + -3y2 = 0
Combine like terms: 3 + 4 = 7
7 + -1y + 1y + 2y2 + -3y2 = 0
Combine like terms: -1y + 1y = 0
7 + 0 + 2y2 + -3y2 = 0
7 + 2y2 + -3y2 = 0
Combine like terms: 2y2 + -3y2 = -1y2
7 + -1y2 = 0
Solving
7 + -1y2 = 0
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -1y2 = 0 + -7
Combine like terms: 7 + -7 = 0
0 + -1y2 = 0 + -7
-1y2 = 0 + -7
Combine like terms: 0 + -7 = -7
-1y2 = -7
Divide each side by '-1'.
y2 = 7
Simplifying
y2 = 7
Take the square root of each side:
y = {-2.645751311, 2.645751311}
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