4x(2x+3)-2(x+4)=

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


Simplifying
4x(2x + 3) + -2(x + 4) = 0

Reorder the terms:
4x(3 + 2x) + -2(x + 4) = 0
(3 * 4x + 2x * 4x) + -2(x + 4) = 0
(12x + 8x2) + -2(x + 4) = 0

Reorder the terms:
12x + 8x2 + -2(4 + x) = 0
12x + 8x2 + (4 * -2 + x * -2) = 0
12x + 8x2 + (-8 + -2x) = 0

Reorder the terms:
-8 + 12x + -2x + 8x2 = 0

Combine like terms: 12x + -2x = 10x
-8 + 10x + 8x2 = 0

Solving
-8 + 10x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 5x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-4 + 5x + 4x2 = 0

Solving
-4 + 5x + 4x2 = 0

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

Divide each side by '4'.
-1 + 1.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.25x + x2 = 0 + 1
1.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.25x + x2 = 1

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 1 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 1 + 0.390625

Combine like terms: 1 + 0.390625 = 1.390625
0.390625 + 1.25x + x2 = 1.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(x + 0.625) equal to 1.179247642 and -1.179247642.


Subproblem 1
x + 0.625 = 1.179247642

Simplifying
x + 0.625 = 1.179247642

Reorder the terms:
0.625 + x = 1.179247642

Solving
0.625 + x = 1.179247642

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 1.179247642 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 1.179247642 + -0.625
x = 1.179247642 + -0.625

Combine like terms: 1.179247642 + -0.625 = 0.554247642
x = 0.554247642

Simplifying
x = 0.554247642


Subproblem 2
x + 0.625 = -1.179247642

Simplifying
x + 0.625 = -1.179247642

Reorder the terms:
0.625 + x = -1.179247642

Solving
0.625 + x = -1.179247642

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -1.179247642 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -1.179247642 + -0.625
x = -1.179247642 + -0.625

Combine like terms: -1.179247642 + -0.625 = -1.804247642
x = -1.804247642

Simplifying
x = -1.804247642


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.554247642, -1.804247642}
Solution
x = {0.554247642, -1.804247642}

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