-2(3+x)5x=-24

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Solution for -2(3+x)5x=-24 equation: 


Simplifying
-2(3 + x) * 5x = -24

Reorder the terms for easier multiplication:
-2 * 5x(3 + x) = -24

Multiply -2 * 5
-10x(3 + x) = -24
(3 * -10x + x * -10x) = -24
(-30x + -10x2) = -24

Solving
-30x + -10x2 = -24

Solving for variable 'x'.

Reorder the terms:
24 + -30x + -10x2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + -30x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -15x + -5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(12 + -15x + -5x2)' equal to zero and attempt to solve:

Simplifying
12 + -15x + -5x2 = 0

Solving
12 + -15x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2.4 + 3x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 3x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 3x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 3x + x2 = 0 + 2.4
3x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
3x + x2 = 2.4

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2.4 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2.4 + 2.25

Combine like terms: 2.4 + 2.25 = 4.65
2.25 + 3x + x2 = 4.65

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.65

Calculate the square root of the right side: 2.156385865

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.156385865 and -2.156385865.


Subproblem 1
x + 1.5 = 2.156385865

Simplifying
x + 1.5 = 2.156385865

Reorder the terms:
1.5 + x = 2.156385865

Solving
1.5 + x = 2.156385865

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.156385865 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.156385865 + -1.5
x = 2.156385865 + -1.5

Combine like terms: 2.156385865 + -1.5 = 0.656385865
x = 0.656385865

Simplifying
x = 0.656385865


Subproblem 2
x + 1.5 = -2.156385865

Simplifying
x + 1.5 = -2.156385865

Reorder the terms:
1.5 + x = -2.156385865

Solving
1.5 + x = -2.156385865

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.156385865 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.156385865 + -1.5
x = -2.156385865 + -1.5

Combine like terms: -2.156385865 + -1.5 = -3.656385865
x = -3.656385865

Simplifying
x = -3.656385865


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.656385865, -3.656385865}
Solution
x = {0.656385865, -3.656385865}

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