2(5x-4)=4x(6-1x)

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Solution for 2(5x-4)=4x(6-1x) equation: 


Simplifying
2(5x + -4) = 4x(6 + -1x)

Reorder the terms:
2(-4 + 5x) = 4x(6 + -1x)
(-4 * 2 + 5x * 2) = 4x(6 + -1x)
(-8 + 10x) = 4x(6 + -1x)
-8 + 10x = (6 * 4x + -1x * 4x)
-8 + 10x = (24x + -4x2)

Solving
-8 + 10x = 24x + -4x2

Solving for variable 'x'.

Combine like terms: 10x + -24x = -14x
-8 + -14x + 4x2 = 24x + -4x2 + -24x + 4x2

Reorder the terms:
-8 + -14x + 4x2 = 24x + -24x + -4x2 + 4x2

Combine like terms: 24x + -24x = 0
-8 + -14x + 4x2 = 0 + -4x2 + 4x2
-8 + -14x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-8 + -14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -7x + 2x2) = 0

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

Ignore the factor 2.

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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.5, 4}

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