(2*x+1)*(x-3)=(x-1)(x+5)-(3*x+2)*(x-1)

Solution for (2*x+1)*(x-3)=(x-1)(x+5)-(3*x+2)*(x-1) equation:

Simplifying
(2x + 1)(x + -3) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)

Reorder the terms:
(1 + 2x)(x + -3) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)

Reorder the terms:
(1 + 2x)(-3 + x) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)

Multiply (1 + 2x) * (-3 + x)
(1(-3 + x) + 2x * (-3 + x)) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)
((-3 * 1 + x * 1) + 2x * (-3 + x)) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)
((-3 + 1x) + 2x * (-3 + x)) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)
(-3 + 1x + (-3 * 2x + x * 2x)) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)
(-3 + 1x + (-6x + 2x2)) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)

Combine like terms: 1x + -6x = -5x
(-3 + -5x + 2x2) = (x + -1)(x + 5) + -1(3x + 2)(x + -1)

Reorder the terms:
-3 + -5x + 2x2 = (-1 + x)(x + 5) + -1(3x + 2)(x + -1)

Reorder the terms:
-3 + -5x + 2x2 = (-1 + x)(5 + x) + -1(3x + 2)(x + -1)

Multiply (-1 + x) * (5 + x)
-3 + -5x + 2x2 = (-1(5 + x) + x(5 + x)) + -1(3x + 2)(x + -1)
-3 + -5x + 2x2 = ((5 * -1 + x * -1) + x(5 + x)) + -1(3x + 2)(x + -1)
-3 + -5x + 2x2 = ((-5 + -1x) + x(5 + x)) + -1(3x + 2)(x + -1)
-3 + -5x + 2x2 = (-5 + -1x + (5 * x + x * x)) + -1(3x + 2)(x + -1)
-3 + -5x + 2x2 = (-5 + -1x + (5x + x2)) + -1(3x + 2)(x + -1)

Combine like terms: -1x + 5x = 4x
-3 + -5x + 2x2 = (-5 + 4x + x2) + -1(3x + 2)(x + -1)

Reorder the terms:
-3 + -5x + 2x2 = -5 + 4x + x2 + -1(2 + 3x)(x + -1)

Reorder the terms:
-3 + -5x + 2x2 = -5 + 4x + x2 + -1(2 + 3x)(-1 + x)

Multiply (2 + 3x) * (-1 + x)
-3 + -5x + 2x2 = -5 + 4x + x2 + -1(2(-1 + x) + 3x * (-1 + x))
-3 + -5x + 2x2 = -5 + 4x + x2 + -1((-1 * 2 + x * 2) + 3x * (-1 + x))
-3 + -5x + 2x2 = -5 + 4x + x2 + -1((-2 + 2x) + 3x * (-1 + x))
-3 + -5x + 2x2 = -5 + 4x + x2 + -1(-2 + 2x + (-1 * 3x + x * 3x))
-3 + -5x + 2x2 = -5 + 4x + x2 + -1(-2 + 2x + (-3x + 3x2))

Combine like terms: 2x + -3x = -1x
-3 + -5x + 2x2 = -5 + 4x + x2 + -1(-2 + -1x + 3x2)
-3 + -5x + 2x2 = -5 + 4x + x2 + (-2 * -1 + -1x * -1 + 3x2 * -1)
-3 + -5x + 2x2 = -5 + 4x + x2 + (2 + 1x + -3x2)

Reorder the terms:
-3 + -5x + 2x2 = -5 + 2 + 4x + 1x + x2 + -3x2

Combine like terms: -5 + 2 = -3
-3 + -5x + 2x2 = -3 + 4x + 1x + x2 + -3x2

Combine like terms: 4x + 1x = 5x
-3 + -5x + 2x2 = -3 + 5x + x2 + -3x2

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

Add '3' to each side of the equation.
-3 + -5x + 3 + 2x2 = -3 + 5x + 3 + -2x2

Reorder the terms:
-3 + 3 + -5x + 2x2 = -3 + 5x + 3 + -2x2

Combine like terms: -3 + 3 = 0
0 + -5x + 2x2 = -3 + 5x + 3 + -2x2
-5x + 2x2 = -3 + 5x + 3 + -2x2

Reorder the terms:
-5x + 2x2 = -3 + 3 + 5x + -2x2

Combine like terms: -3 + 3 = 0
-5x + 2x2 = 0 + 5x + -2x2
-5x + 2x2 = 5x + -2x2

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

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

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}