5x(4x+6)=-4

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Solution for 5x(4x+6)=-4 equation: 


Simplifying
5x(4x + 6) = -4

Reorder the terms:
5x(6 + 4x) = -4
(6 * 5x + 4x * 5x) = -4
(30x + 20x2) = -4

Solving
30x + 20x2 = -4

Solving for variable 'x'.

Reorder the terms:
4 + 30x + 20x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 30x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 15x + 10x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 15x + 10x2)' equal to zero and attempt to solve:

Simplifying
2 + 15x + 10x2 = 0

Solving
2 + 15x + 10x2 = 0

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

Divide each side by '10'.
0.2 + 1.5x + x2 = 0.0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.5x + -0.2 + x2 = 0.0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.5x + x2 = 0.0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.5x + x2 = 0.0 + -0.2
1.5x + x2 = 0.0 + -0.2

Combine like terms: 0.0 + -0.2 = -0.2
1.5x + x2 = -0.2

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -0.2 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.2 + 0.5625

Combine like terms: -0.2 + 0.5625 = 0.3625
0.5625 + 1.5x + x2 = 0.3625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.3625

Calculate the square root of the right side: 0.602079729

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.602079729 and -0.602079729.


Subproblem 1
x + 0.75 = 0.602079729

Simplifying
x + 0.75 = 0.602079729

Reorder the terms:
0.75 + x = 0.602079729

Solving
0.75 + x = 0.602079729

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 0.602079729 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.602079729 + -0.75
x = 0.602079729 + -0.75

Combine like terms: 0.602079729 + -0.75 = -0.147920271
x = -0.147920271

Simplifying
x = -0.147920271


Subproblem 2
x + 0.75 = -0.602079729

Simplifying
x + 0.75 = -0.602079729

Reorder the terms:
0.75 + x = -0.602079729

Solving
0.75 + x = -0.602079729

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -0.602079729 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.602079729 + -0.75
x = -0.602079729 + -0.75

Combine like terms: -0.602079729 + -0.75 = -1.352079729
x = -1.352079729

Simplifying
x = -1.352079729


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.147920271, -1.352079729}
Solution
x = {-0.147920271, -1.352079729}

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