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

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


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

Reorder the terms:
3x(-2 + x) = (2x + 5)(x + -2)
(-2 * 3x + x * 3x) = (2x + 5)(x + -2)
(-6x + 3x2) = (2x + 5)(x + -2)

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

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

Multiply (5 + 2x) * (-2 + x)
-6x + 3x2 = (5(-2 + x) + 2x * (-2 + x))
-6x + 3x2 = ((-2 * 5 + x * 5) + 2x * (-2 + x))
-6x + 3x2 = ((-10 + 5x) + 2x * (-2 + x))
-6x + 3x2 = (-10 + 5x + (-2 * 2x + x * 2x))
-6x + 3x2 = (-10 + 5x + (-4x + 2x2))

Combine like terms: 5x + -4x = 1x
-6x + 3x2 = (-10 + 1x + 2x2)

Solving
-6x + 3x2 = -10 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
10 + -6x + -1x + 3x2 + -2x2 = -10 + 1x + 2x2 + 10 + -1x + -2x2

Combine like terms: -6x + -1x = -7x
10 + -7x + 3x2 + -2x2 = -10 + 1x + 2x2 + 10 + -1x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
10 + -7x + 1x2 = -10 + 1x + 2x2 + 10 + -1x + -2x2

Reorder the terms:
10 + -7x + 1x2 = -10 + 10 + 1x + -1x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
10 + -7x + 1x2 = 0 + 1x + -1x + 2x2 + -2x2
10 + -7x + 1x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
10 + -7x + 1x2 = 0 + 2x2 + -2x2
10 + -7x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + -7x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(5 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2, 5}

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