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Simplifying
3(2y2 + -4) + -1(2y2 + 7) * 4 = 2(5 + -2y2)
Reorder the terms:
3(-4 + 2y2) + -1(2y2 + 7) * 4 = 2(5 + -2y2)
(-4 * 3 + 2y2 * 3) + -1(2y2 + 7) * 4 = 2(5 + -2y2)
(-12 + 6y2) + -1(2y2 + 7) * 4 = 2(5 + -2y2)
Reorder the terms:
-12 + 6y2 + -1(7 + 2y2) * 4 = 2(5 + -2y2)
Reorder the terms for easier multiplication:
-12 + 6y2 + -1 * 4(7 + 2y2) = 2(5 + -2y2)
Multiply -1 * 4
-12 + 6y2 + -4(7 + 2y2) = 2(5 + -2y2)
-12 + 6y2 + (7 * -4 + 2y2 * -4) = 2(5 + -2y2)
-12 + 6y2 + (-28 + -8y2) = 2(5 + -2y2)
Reorder the terms:
-12 + -28 + 6y2 + -8y2 = 2(5 + -2y2)
Combine like terms: -12 + -28 = -40
-40 + 6y2 + -8y2 = 2(5 + -2y2)
Combine like terms: 6y2 + -8y2 = -2y2
-40 + -2y2 = 2(5 + -2y2)
-40 + -2y2 = (5 * 2 + -2y2 * 2)
-40 + -2y2 = (10 + -4y2)
Solving
-40 + -2y2 = 10 + -4y2
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '4y2' to each side of the equation.
-40 + -2y2 + 4y2 = 10 + -4y2 + 4y2
Combine like terms: -2y2 + 4y2 = 2y2
-40 + 2y2 = 10 + -4y2 + 4y2
Combine like terms: -4y2 + 4y2 = 0
-40 + 2y2 = 10 + 0
-40 + 2y2 = 10
Add '40' to each side of the equation.
-40 + 40 + 2y2 = 10 + 40
Combine like terms: -40 + 40 = 0
0 + 2y2 = 10 + 40
2y2 = 10 + 40
Combine like terms: 10 + 40 = 50
2y2 = 50
Divide each side by '2'.
y2 = 25
Simplifying
y2 = 25
Take the square root of each side:
y = {-5, 5}
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