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

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

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

Combine like terms: 5 + -2 = 3
2(3) + x = 2x(5 + -3x)

Multiply 2 * 3
6 + x = 2x(5 + -3x)
6 + x = (5 * 2x + -3x * 2x)
6 + x = (10x + -6x2)

Solving
6 + x = 10x + -6x2

Solving for variable 'x'.

Combine like terms: x + -10x = -9x
6 + -9x + 6x2 = 10x + -6x2 + -10x + 6x2

Reorder the terms:
6 + -9x + 6x2 = 10x + -10x + -6x2 + 6x2

Combine like terms: 10x + -10x = 0
6 + -9x + 6x2 = 0 + -6x2 + 6x2
6 + -9x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
6 + -9x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -3x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -3x + 2x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x + 2x2 = 0

Solving
2 + -3x + 2x2 = 0

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

Divide each side by '2'.
1 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.5x + x2 = 0 + -1
-1.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.5x + x2 = -1

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -1 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -1 + 0.5625

Combine like terms: -1 + 0.5625 = -0.4375
0.5625 + -1.5x + x2 = -0.4375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -0.4375

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.