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

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


Simplifying
2(5 + -2x) = 4x(x + -2) + -5
(5 * 2 + -2x * 2) = 4x(x + -2) + -5
(10 + -4x) = 4x(x + -2) + -5

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

Reorder the terms:
10 + -4x = -5 + -8x + 4x2

Solving
10 + -4x = -5 + -8x + 4x2

Solving for variable 'x'.

Reorder the terms:
10 + 5 + -4x + 8x + -4x2 = -5 + -8x + 4x2 + 5 + 8x + -4x2

Combine like terms: 10 + 5 = 15
15 + -4x + 8x + -4x2 = -5 + -8x + 4x2 + 5 + 8x + -4x2

Combine like terms: -4x + 8x = 4x
15 + 4x + -4x2 = -5 + -8x + 4x2 + 5 + 8x + -4x2

Reorder the terms:
15 + 4x + -4x2 = -5 + 5 + -8x + 8x + 4x2 + -4x2

Combine like terms: -5 + 5 = 0
15 + 4x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2
15 + 4x + -4x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
15 + 4x + -4x2 = 0 + 4x2 + -4x2
15 + 4x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
15 + 4x + -4x2 = 0

Factor a trinomial.
(5 + -2x)(3 + 2x) = 0


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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {2.5, -1.5}

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