What are the solutions to the equation 42x^3+30x^2=21x+15 ?

The solutions to the equation 42x^3+30x^2=21x+15 are x=-5/7 ,x=-1/(sqrt(2)),x= 1/(sqrt(2))

Find the zeros of 42x^3+30x^2=21x+15

The zeros of 42x^3+30x^2=21x+15 are x=-5/7 ,x=-1/(sqrt(2)),x= 1/(sqrt(2))

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42 x^{3} + 30 x^{2} = 21 x + 15

x = - \frac{5}{7}, x = - \frac{1}{2}, x = \frac{1}{2}

Decimal Notation

x = - 0.71428 \dots, x = - 0.70710 \dots, x = 0.70710 \dots

Solution steps

42 x^{3} + 30 x^{2} = 21 x + 15

Move

15

to the left side

42 x^{3} + 30 x^{2} - 15 = 21 x

Move

21 x

to the left side

42 x^{3} + 30 x^{2} - 15 - 21 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

42 x^{3} + 30 x^{2} - 21 x - 15 = 0

Factor

42 x^{3} + 30 x^{2} - 21 x - 15 : 3 (7 x + 5) (2 x + 1) (2 x - 1)

3 (7 x + 5) (2 x + 1) (2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

7 x + 5 = 0 or 2 x + 1 = 0 or 2 x - 1 = 0

Solve

7 x + 5 = 0 : x = - \frac{5}{7}

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

Solve

2 x - 1 = 0 : x = \frac{1}{2}

The solutions are

x = - \frac{5}{7}, x = - \frac{1}{2}, x = \frac{1}{2}

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

0 = 9 t - t^{3}

x^{4} + 3 = 84

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

- y (1 + y^{2}) = 0

What are the solutions to the equation 42x^3+30x^2=21x+15 ?
The solutions to the equation 42x^3+30x^2=21x+15 are x=-5/7 ,x=-1/(sqrt(2)),x= 1/(sqrt(2))
Find the zeros of 42x^3+30x^2=21x+15
The zeros of 42x^3+30x^2=21x+15 are x=-5/7 ,x=-1/(sqrt(2)),x= 1/(sqrt(2))