What are the solutions to the equation 2c^4-6c^3=12c^2-36c ?

The solutions to the equation 2c^4-6c^3=12c^2-36c are c=0,c=3,c=-sqrt(6),c=sqrt(6)

Find the zeros of 2c^4-6c^3=12c^2-36c

The zeros of 2c^4-6c^3=12c^2-36c are c=0,c=3,c=-sqrt(6),c=sqrt(6)

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2 c^{4} - 6 c^{3} = 12 c^{2} - 36 c

c = 0, c = 3, c = - 6, c = 6

Decimal

c = 0, c = 3, c = - 2.44948 \dots, c = 2.44948 \dots

Solution steps

2 c^{4} - 6 c^{3} = 12 c^{2} - 36 c

Move

36 c

to the left side

2 c^{4} - 6 c^{3} + 36 c = 12 c^{2}

Move

12 c^{2}

to the left side

2 c^{4} - 6 c^{3} + 36 c - 12 c^{2} = 0

Factor

2 c^{4} - 6 c^{3} + 36 c - 12 c^{2} : 2 c (c - 3) (c + 6) (c - 6)

2 c (c - 3) (c + 6) (c - 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

c = 0 or c - 3 = 0 or c + 6 = 0 or c - 6 = 0

Solve

c - 3 = 0 : c = 3

Solve

c + 6 = 0 : c = - 6

Solve

c - 6 = 0 : c = 6

The solutions are

c = 0, c = 3, c = - 6, c = 6

x^{4} - 6 x^{3} + 17 x^{2} - 24 x + 52 = 0

x^{2} (x^{2} - 16) - (x^{2} - 16) = 0

1 + x + 2 x^{2} + 3 x^{3} + 4 x^{4} = 0

4 x^{2} (x + 8) = 0

6 x 1 9^{2} - 174 x^{19} + 1140 = 0

What are the solutions to the equation 2c^4-6c^3=12c^2-36c ?
The solutions to the equation 2c^4-6c^3=12c^2-36c are c=0,c=3,c=-sqrt(6),c=sqrt(6)
Find the zeros of 2c^4-6c^3=12c^2-36c
The zeros of 2c^4-6c^3=12c^2-36c are c=0,c=3,c=-sqrt(6),c=sqrt(6)