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

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


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

Reorder the terms:
5x(-2 + x) = (2x + 1)(x + -2)
(-2 * 5x + x * 5x) = (2x + 1)(x + -2)
(-10x + 5x2) = (2x + 1)(x + -2)

Reorder the terms:
-10x + 5x2 = (1 + 2x)(x + -2)

Reorder the terms:
-10x + 5x2 = (1 + 2x)(-2 + x)

Multiply (1 + 2x) * (-2 + x)
-10x + 5x2 = (1(-2 + x) + 2x * (-2 + x))
-10x + 5x2 = ((-2 * 1 + x * 1) + 2x * (-2 + x))
-10x + 5x2 = ((-2 + 1x) + 2x * (-2 + x))
-10x + 5x2 = (-2 + 1x + (-2 * 2x + x * 2x))
-10x + 5x2 = (-2 + 1x + (-4x + 2x2))

Combine like terms: 1x + -4x = -3x
-10x + 5x2 = (-2 + -3x + 2x2)

Solving
-10x + 5x2 = -2 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + -10x + 3x + 5x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

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

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

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

Combine like terms: -2 + 2 = 0
2 + -7x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2
2 + -7x + 3x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
2 + -7x + 3x2 = 0 + 2x2 + -2x2
2 + -7x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + -7x + 3x2 = 0

Factor a trinomial.
(1 + -3x)(2 + -1x) = 0


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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.3333333333, 2}

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