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Simplifying
135 = (2y + 3)(2y + -3)
Reorder the terms:
135 = (3 + 2y)(2y + -3)
Reorder the terms:
135 = (3 + 2y)(-3 + 2y)
Multiply (3 + 2y) * (-3 + 2y)
135 = (3(-3 + 2y) + 2y * (-3 + 2y))
135 = ((-3 * 3 + 2y * 3) + 2y * (-3 + 2y))
135 = ((-9 + 6y) + 2y * (-3 + 2y))
135 = (-9 + 6y + (-3 * 2y + 2y * 2y))
135 = (-9 + 6y + (-6y + 4y2))
Combine like terms: 6y + -6y = 0
135 = (-9 + 0 + 4y2)
135 = (-9 + 4y2)
Solving
135 = -9 + 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.
135 + -4y2 = -9 + 4y2 + -4y2
Combine like terms: 4y2 + -4y2 = 0
135 + -4y2 = -9 + 0
135 + -4y2 = -9
Add '-135' to each side of the equation.
135 + -135 + -4y2 = -9 + -135
Combine like terms: 135 + -135 = 0
0 + -4y2 = -9 + -135
-4y2 = -9 + -135
Combine like terms: -9 + -135 = -144
-4y2 = -144
Divide each side by '-4'.
y2 = 36
Simplifying
y2 = 36
Take the square root of each side:
y = {-6, 6}
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