5[2-x(2x-4)]=2(5-3x)

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Solution for 5[2-x(2x-4)]=2(5-3x) equation: 


Simplifying
5[2 + -1x(2x + -4)] = 2(5 + -3x)

Reorder the terms:
5[2 + -1x(-4 + 2x)] = 2(5 + -3x)
5[2 + (-4 * -1x + 2x * -1x)] = 2(5 + -3x)
5[2 + (4x + -2x2)] = 2(5 + -3x)
[2 * 5 + 4x * 5 + -2x2 * 5] = 2(5 + -3x)
[10 + 20x + -10x2] = 2(5 + -3x)
10 + 20x + -10x2 = (5 * 2 + -3x * 2)
10 + 20x + -10x2 = (10 + -6x)

Add '-10' to each side of the equation.
10 + 20x + -10 + -10x2 = 10 + -10 + -6x

Reorder the terms:
10 + -10 + 20x + -10x2 = 10 + -10 + -6x

Combine like terms: 10 + -10 = 0
0 + 20x + -10x2 = 10 + -10 + -6x
20x + -10x2 = 10 + -10 + -6x

Combine like terms: 10 + -10 = 0
20x + -10x2 = 0 + -6x
20x + -10x2 = -6x

Solving
20x + -10x2 = -6x

Solving for variable 'x'.

Reorder the terms:
20x + 6x + -10x2 = -6x + 6x

Combine like terms: 20x + 6x = 26x
26x + -10x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
26x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(13 + -5x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(13 + -5x)' equal to zero and attempt to solve:

Simplifying
13 + -5x = 0

Solving
13 + -5x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -5x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -5x = 0 + -13
-5x = 0 + -13

Combine like terms: 0 + -13 = -13
-5x = -13

Divide each side by '-5'.
x = 2.6

Simplifying
x = 2.6
Solution
x = {0, 2.6}

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