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

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


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

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

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

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

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

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

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

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

Combine like terms: 10x + -3x = 7x
-2 + 3x + 2x2 = (-6 + 7x + 5x2)

Solving
-2 + 3x + 2x2 = -6 + 7x + 5x2

Solving for variable 'x'.

Reorder the terms:
-2 + 6 + 3x + -7x + 2x2 + -5x2 = -6 + 7x + 5x2 + 6 + -7x + -5x2

Combine like terms: -2 + 6 = 4
4 + 3x + -7x + 2x2 + -5x2 = -6 + 7x + 5x2 + 6 + -7x + -5x2

Combine like terms: 3x + -7x = -4x
4 + -4x + 2x2 + -5x2 = -6 + 7x + 5x2 + 6 + -7x + -5x2

Combine like terms: 2x2 + -5x2 = -3x2
4 + -4x + -3x2 = -6 + 7x + 5x2 + 6 + -7x + -5x2

Reorder the terms:
4 + -4x + -3x2 = -6 + 6 + 7x + -7x + 5x2 + -5x2

Combine like terms: -6 + 6 = 0
4 + -4x + -3x2 = 0 + 7x + -7x + 5x2 + -5x2
4 + -4x + -3x2 = 7x + -7x + 5x2 + -5x2

Combine like terms: 7x + -7x = 0
4 + -4x + -3x2 = 0 + 5x2 + -5x2
4 + -4x + -3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
4 + -4x + -3x2 = 0

Factor a trinomial.
(2 + -3x)(2 + x) = 0


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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {0.6666666667, -2}

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