(2x-4)(x-10)=(x+6)(x-10)

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Solution for (2x-4)(x-10)=(x+6)(x-10) equation: 


Simplifying
(2x + -4)(x + -10) = (x + 6)(x + -10)

Reorder the terms:
(-4 + 2x)(x + -10) = (x + 6)(x + -10)

Reorder the terms:
(-4 + 2x)(-10 + x) = (x + 6)(x + -10)

Multiply (-4 + 2x) * (-10 + x)
(-4(-10 + x) + 2x * (-10 + x)) = (x + 6)(x + -10)
((-10 * -4 + x * -4) + 2x * (-10 + x)) = (x + 6)(x + -10)
((40 + -4x) + 2x * (-10 + x)) = (x + 6)(x + -10)
(40 + -4x + (-10 * 2x + x * 2x)) = (x + 6)(x + -10)
(40 + -4x + (-20x + 2x2)) = (x + 6)(x + -10)

Combine like terms: -4x + -20x = -24x
(40 + -24x + 2x2) = (x + 6)(x + -10)

Reorder the terms:
40 + -24x + 2x2 = (6 + x)(x + -10)

Reorder the terms:
40 + -24x + 2x2 = (6 + x)(-10 + x)

Multiply (6 + x) * (-10 + x)
40 + -24x + 2x2 = (6(-10 + x) + x(-10 + x))
40 + -24x + 2x2 = ((-10 * 6 + x * 6) + x(-10 + x))
40 + -24x + 2x2 = ((-60 + 6x) + x(-10 + x))
40 + -24x + 2x2 = (-60 + 6x + (-10 * x + x * x))
40 + -24x + 2x2 = (-60 + 6x + (-10x + x2))

Combine like terms: 6x + -10x = -4x
40 + -24x + 2x2 = (-60 + -4x + x2)

Solving
40 + -24x + 2x2 = -60 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
40 + 60 + -24x + 4x + 2x2 + -1x2 = -60 + -4x + x2 + 60 + 4x + -1x2

Combine like terms: 40 + 60 = 100
100 + -24x + 4x + 2x2 + -1x2 = -60 + -4x + x2 + 60 + 4x + -1x2

Combine like terms: -24x + 4x = -20x
100 + -20x + 2x2 + -1x2 = -60 + -4x + x2 + 60 + 4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
100 + -20x + 1x2 = -60 + -4x + x2 + 60 + 4x + -1x2

Reorder the terms:
100 + -20x + 1x2 = -60 + 60 + -4x + 4x + x2 + -1x2

Combine like terms: -60 + 60 = 0
100 + -20x + 1x2 = 0 + -4x + 4x + x2 + -1x2
100 + -20x + 1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
100 + -20x + 1x2 = 0 + x2 + -1x2
100 + -20x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
100 + -20x + 1x2 = 0

Factor a trinomial.
(10 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {10, 10}

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