0=5+2x(3+4x)

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Solution for 0=5+2x(3+4x) equation:


Simplifying
0 = 5 + 2x(3 + 4x)
0 = 5 + (3 * 2x + 4x * 2x)
0 = 5 + (6x + 8x2)

Solving
0 = 5 + 6x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -6x + -8x2 = 5 + 6x + 8x2 + -5 + -6x + -8x2

Reorder the terms:
-5 + -6x + -8x2 = 5 + -5 + 6x + -6x + 8x2 + -8x2

Combine like terms: 5 + -5 = 0
-5 + -6x + -8x2 = 0 + 6x + -6x + 8x2 + -8x2
-5 + -6x + -8x2 = 6x + -6x + 8x2 + -8x2

Combine like terms: 6x + -6x = 0
-5 + -6x + -8x2 = 0 + 8x2 + -8x2
-5 + -6x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-5 + -6x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 6x + 8x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 6x + 8x2)' equal to zero and attempt to solve:

Simplifying
5 + 6x + 8x2 = 0

Solving
5 + 6x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.625 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + 0.75x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + 0.75x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + 0.75x + x2 = 0 + -0.625
0.75x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
0.75x + x2 = -0.625

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = -0.625 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -0.625 + 0.140625

Combine like terms: -0.625 + 0.140625 = -0.484375
0.140625 + 0.75x + x2 = -0.484375

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = -0.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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