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

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


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

Reorder the terms:
-2(-2 + 4x) = (2x + 10)(4x + -2)
(-2 * -2 + 4x * -2) = (2x + 10)(4x + -2)
(4 + -8x) = (2x + 10)(4x + -2)

Reorder the terms:
4 + -8x = (10 + 2x)(4x + -2)

Reorder the terms:
4 + -8x = (10 + 2x)(-2 + 4x)

Multiply (10 + 2x) * (-2 + 4x)
4 + -8x = (10(-2 + 4x) + 2x * (-2 + 4x))
4 + -8x = ((-2 * 10 + 4x * 10) + 2x * (-2 + 4x))
4 + -8x = ((-20 + 40x) + 2x * (-2 + 4x))
4 + -8x = (-20 + 40x + (-2 * 2x + 4x * 2x))
4 + -8x = (-20 + 40x + (-4x + 8x2))

Combine like terms: 40x + -4x = 36x
4 + -8x = (-20 + 36x + 8x2)

Solving
4 + -8x = -20 + 36x + 8x2

Solving for variable 'x'.

Reorder the terms:
4 + 20 + -8x + -36x + -8x2 = -20 + 36x + 8x2 + 20 + -36x + -8x2

Combine like terms: 4 + 20 = 24
24 + -8x + -36x + -8x2 = -20 + 36x + 8x2 + 20 + -36x + -8x2

Combine like terms: -8x + -36x = -44x
24 + -44x + -8x2 = -20 + 36x + 8x2 + 20 + -36x + -8x2

Reorder the terms:
24 + -44x + -8x2 = -20 + 20 + 36x + -36x + 8x2 + -8x2

Combine like terms: -20 + 20 = 0
24 + -44x + -8x2 = 0 + 36x + -36x + 8x2 + -8x2
24 + -44x + -8x2 = 36x + -36x + 8x2 + -8x2

Combine like terms: 36x + -36x = 0
24 + -44x + -8x2 = 0 + 8x2 + -8x2
24 + -44x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
24 + -44x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -11x + -2x2) = 0

Factor a trinomial.
4((1 + -2x)(6 + x)) = 0

Ignore the factor 4.

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

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {0.5, -6}

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