3(2x+5)=x(4-2x)+5

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Solution for 3(2x+5)=x(4-2x)+5 equation: 


Simplifying
3(2x + 5) = x(4 + -2x) + 5

Reorder the terms:
3(5 + 2x) = x(4 + -2x) + 5
(5 * 3 + 2x * 3) = x(4 + -2x) + 5
(15 + 6x) = x(4 + -2x) + 5
15 + 6x = (4 * x + -2x * x) + 5
15 + 6x = (4x + -2x2) + 5

Reorder the terms:
15 + 6x = 5 + 4x + -2x2

Solving
15 + 6x = 5 + 4x + -2x2

Solving for variable 'x'.

Reorder the terms:
15 + -5 + 6x + -4x + 2x2 = 5 + 4x + -2x2 + -5 + -4x + 2x2

Combine like terms: 15 + -5 = 10
10 + 6x + -4x + 2x2 = 5 + 4x + -2x2 + -5 + -4x + 2x2

Combine like terms: 6x + -4x = 2x
10 + 2x + 2x2 = 5 + 4x + -2x2 + -5 + -4x + 2x2

Reorder the terms:
10 + 2x + 2x2 = 5 + -5 + 4x + -4x + -2x2 + 2x2

Combine like terms: 5 + -5 = 0
10 + 2x + 2x2 = 0 + 4x + -4x + -2x2 + 2x2
10 + 2x + 2x2 = 4x + -4x + -2x2 + 2x2

Combine like terms: 4x + -4x = 0
10 + 2x + 2x2 = 0 + -2x2 + 2x2
10 + 2x + 2x2 = -2x2 + 2x2

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

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

Ignore the factor 2.

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

Simplifying
5 + x + x2 = 0

Solving
5 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x + x2 = 0 + -5
x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
x + x2 = -5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -5 + 0.25

Reorder the terms:
0.25 + x + x2 = -5 + 0.25

Combine like terms: -5 + 0.25 = -4.75
0.25 + x + x2 = -4.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -4.75

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.

The solution to this equation could not be determined.

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