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

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


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

Reorder the terms:
-4 + 3x = x(2x + 5)

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

Solving
-4 + 3x = 5x + 2x2

Solving for variable 'x'.

Combine like terms: 3x + -5x = -2x
-4 + -2x + -2x2 = 5x + 2x2 + -5x + -2x2

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

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

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

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

Ignore the factor -2.

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

Simplifying
2 + x + x2 = 0

Solving
2 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + x + -2 + x2 = 0 + -2

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

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

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

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 = -2 + 0.25

Reorder the terms:
0.25 + x + x2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + x + x2 = -1.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.75

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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