-18x-4x(2x+5)-12=

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Solution for -18x-4x(2x+5)-12= equation: 


Simplifying
-18x + -4x(2x + 5) + -12 = 0

Reorder the terms:
-18x + -4x(5 + 2x) + -12 = 0
-18x + (5 * -4x + 2x * -4x) + -12 = 0
-18x + (-20x + -8x2) + -12 = 0

Reorder the terms:
-12 + -18x + -20x + -8x2 = 0

Combine like terms: -18x + -20x = -38x
-12 + -38x + -8x2 = 0

Solving
-12 + -38x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(6 + 19x + 4x2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(6 + 19x + 4x2)' equal to zero and attempt to solve:

Simplifying
6 + 19x + 4x2 = 0

Solving
6 + 19x + 4x2 = 0

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

Divide each side by '4'.
1.5 + 4.75x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 4.75x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 4.75x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 4.75x + x2 = 0 + -1.5
4.75x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
4.75x + x2 = -1.5

The x term is 4.75x.  Take half its coefficient (2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
4.75x + 5.640625 + x2 = -1.5 + 5.640625

Reorder the terms:
5.640625 + 4.75x + x2 = -1.5 + 5.640625

Combine like terms: -1.5 + 5.640625 = 4.140625
5.640625 + 4.75x + x2 = 4.140625

Factor a perfect square on the left side:
(x + 2.375)(x + 2.375) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + 2.375) equal to 2.034852575 and -2.034852575.


Subproblem 1
x + 2.375 = 2.034852575

Simplifying
x + 2.375 = 2.034852575

Reorder the terms:
2.375 + x = 2.034852575

Solving
2.375 + x = 2.034852575

Solving for variable 'x'.

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

Add '-2.375' to each side of the equation.
2.375 + -2.375 + x = 2.034852575 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + x = 2.034852575 + -2.375
x = 2.034852575 + -2.375

Combine like terms: 2.034852575 + -2.375 = -0.340147425
x = -0.340147425

Simplifying
x = -0.340147425


Subproblem 2
x + 2.375 = -2.034852575

Simplifying
x + 2.375 = -2.034852575

Reorder the terms:
2.375 + x = -2.034852575

Solving
2.375 + x = -2.034852575

Solving for variable 'x'.

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

Add '-2.375' to each side of the equation.
2.375 + -2.375 + x = -2.034852575 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + x = -2.034852575 + -2.375
x = -2.034852575 + -2.375

Combine like terms: -2.034852575 + -2.375 = -4.409852575
x = -4.409852575

Simplifying
x = -4.409852575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.340147425, -4.409852575}
Solution
x = {-0.340147425, -4.409852575}

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