4x^3+8x^2+7x=0

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Solution for 4x^3+8x^2+7x=0 equation: 


Simplifying
4x3 + 8x2 + 7x = 0

Reorder the terms:
7x + 8x2 + 4x3 = 0

Solving
7x + 8x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 8x + 4x2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 8x + 4x2)' equal to zero and attempt to solve:

Simplifying
7 + 8x + 4x2 = 0

Solving
7 + 8x + 4x2 = 0

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

Divide each side by '4'.
1.75 + 2x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 2x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 2x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 2x + x2 = 0 + -1.75
2x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
2x + x2 = -1.75

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -1.75 + 1

Reorder the terms:
1 + 2x + x2 = -1.75 + 1

Combine like terms: -1.75 + 1 = -0.75
1 + 2x + x2 = -0.75

Factor a perfect square on the left side:
(x + 1)(x + 1) = -0.75

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.
Solution
x = {0}

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