The four solution values of x of 3x4 + 7x3 + 4x2 = 0 are:
x = -11/3, -1, 0 (repeated)
3x4 + 7x3 + 4x2 = 0
⇒ x2(3x2 + 7x + 4) = 0
⇒ x2(3x + 4)(x + 1) = 0
⇒ x2 = 0 → x = 0 (repeated)
or (3x + 4) = 0 → x = -4/3 = -11/3
or (x + 1) = 0 → x = -1
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4x2 - 2x = 0
4x2+50x = 0 4x(x+12.5) = 0 x = 0 or x = -12.5
4x2-2x = 0 2x(2x-1) = 0 x = 0 or x =1/2
The first equality is: x2 - 5 = -4x2 which gives 5x2 - 5 = 0 which is equivalent to x2 - 5 = 0 The second equality is: -4x2 = 3x which gives 4x2 + 3x = 0 The two results are inconsistent.
4x2 - 13 x + 3 = 0 (4x - 1)(x - 3) = 0 x = 3, 1/4