What are the solutions to the equation 4x+3=x^3+3x^2-9x+12 ?

The solutions to the equation 4x+3=x^3+3x^2-9x+12 are x=1,x=-2+sqrt(13),x=-2-sqrt(13)

Find the zeros of 4x+3=x^3+3x^2-9x+12

The zeros of 4x+3=x^3+3x^2-9x+12 are x=1,x=-2+sqrt(13),x=-2-sqrt(13)

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4 x + 3 = x^{3} + 3 x^{2} - 9 x + 12

x = 1, x = - 2 + 13, x = - 2 - 13

Decimal Notation

x = 1, x = 1.60555 \dots, x = - 5.60555 \dots

Solution steps

4 x + 3 = x^{3} + 3 x^{2} - 9 x + 12

Switch sides

x^{3} + 3 x^{2} - 9 x + 12 = 4 x + 3

Move

3

to the left side

x^{3} + 3 x^{2} - 9 x + 9 = 4 x

Move

4 x

to the left side

x^{3} + 3 x^{2} - 13 x + 9 = 0

Factor

x^{3} + 3 x^{2} - 13 x + 9 : (x - 1) (x^{2} + 4 x - 9)

(x - 1) (x^{2} + 4 x - 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + 4 x - 9 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + 4 x - 9 = 0 : x = - 2 + 13, x = - 2 - 13

The solutions are

x = 1, x = - 2 + 13, x = - 2 - 13

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

(x^{2} - 5 x + 6) (x^{2} + 5 x + 6) - 2 x^{2} = 0

1 - 3 t^{2} - 3 t + t^{3} = 0

20 x^{4} - 5 x^{3} - 12 x^{2} + 3 x = 0

2 x^{3} + 2 x^{2} - 8 x + 12 = 0

What are the solutions to the equation 4x+3=x^3+3x^2-9x+12 ?
The solutions to the equation 4x+3=x^3+3x^2-9x+12 are x=1,x=-2+sqrt(13),x=-2-sqrt(13)
Find the zeros of 4x+3=x^3+3x^2-9x+12
The zeros of 4x+3=x^3+3x^2-9x+12 are x=1,x=-2+sqrt(13),x=-2-sqrt(13)