8x^3+61=(2x+1)(2x+1)(2x+1)

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Solution for 8x^3+61=(2x+1)(2x+1)(2x+1) equation: 


Simplifying
8x3 + 61 = (2x + 1)(2x + 1)(2x + 1)

Reorder the terms:
61 + 8x3 = (2x + 1)(2x + 1)(2x + 1)

Reorder the terms:
61 + 8x3 = (1 + 2x)(2x + 1)(2x + 1)

Reorder the terms:
61 + 8x3 = (1 + 2x)(1 + 2x)(2x + 1)

Reorder the terms:
61 + 8x3 = (1 + 2x)(1 + 2x)(1 + 2x)

Multiply (1 + 2x) * (1 + 2x)
61 + 8x3 = (1(1 + 2x) + 2x * (1 + 2x))(1 + 2x)
61 + 8x3 = ((1 * 1 + 2x * 1) + 2x * (1 + 2x))(1 + 2x)
61 + 8x3 = ((1 + 2x) + 2x * (1 + 2x))(1 + 2x)
61 + 8x3 = (1 + 2x + (1 * 2x + 2x * 2x))(1 + 2x)
61 + 8x3 = (1 + 2x + (2x + 4x2))(1 + 2x)

Combine like terms: 2x + 2x = 4x
61 + 8x3 = (1 + 4x + 4x2)(1 + 2x)

Multiply (1 + 4x + 4x2) * (1 + 2x)
61 + 8x3 = (1(1 + 2x) + 4x * (1 + 2x) + 4x2 * (1 + 2x))
61 + 8x3 = ((1 * 1 + 2x * 1) + 4x * (1 + 2x) + 4x2 * (1 + 2x))
61 + 8x3 = ((1 + 2x) + 4x * (1 + 2x) + 4x2 * (1 + 2x))
61 + 8x3 = (1 + 2x + (1 * 4x + 2x * 4x) + 4x2 * (1 + 2x))
61 + 8x3 = (1 + 2x + (4x + 8x2) + 4x2 * (1 + 2x))
61 + 8x3 = (1 + 2x + 4x + 8x2 + (1 * 4x2 + 2x * 4x2))
61 + 8x3 = (1 + 2x + 4x + 8x2 + (4x2 + 8x3))

Combine like terms: 2x + 4x = 6x
61 + 8x3 = (1 + 6x + 8x2 + 4x2 + 8x3)

Combine like terms: 8x2 + 4x2 = 12x2
61 + 8x3 = (1 + 6x + 12x2 + 8x3)

Add '-8x3' to each side of the equation.
61 + 8x3 + -8x3 = 1 + 6x + 12x2 + 8x3 + -8x3

Combine like terms: 8x3 + -8x3 = 0
61 + 0 = 1 + 6x + 12x2 + 8x3 + -8x3
61 = 1 + 6x + 12x2 + 8x3 + -8x3

Combine like terms: 8x3 + -8x3 = 0
61 = 1 + 6x + 12x2 + 0
61 = 1 + 6x + 12x2

Solving
61 = 1 + 6x + 12x2

Solving for variable 'x'.

Combine like terms: 61 + -1 = 60
60 + -6x + -12x2 = 1 + 6x + 12x2 + -1 + -6x + -12x2

Reorder the terms:
60 + -6x + -12x2 = 1 + -1 + 6x + -6x + 12x2 + -12x2

Combine like terms: 1 + -1 = 0
60 + -6x + -12x2 = 0 + 6x + -6x + 12x2 + -12x2
60 + -6x + -12x2 = 6x + -6x + 12x2 + -12x2

Combine like terms: 6x + -6x = 0
60 + -6x + -12x2 = 0 + 12x2 + -12x2
60 + -6x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
60 + -6x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(10 + -1x + -2x2) = 0

Factor a trinomial.
6((2 + -1x)(5 + 2x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {2, -2.5}

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