(10x-5)(2x+1)=3(3-6x)(4-2x)

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Solution for (10x-5)(2x+1)=3(3-6x)(4-2x) equation: 


Simplifying
(10x + -5)(2x + 1) = 3(3 + -6x)(4 + -2x)

Reorder the terms:
(-5 + 10x)(2x + 1) = 3(3 + -6x)(4 + -2x)

Reorder the terms:
(-5 + 10x)(1 + 2x) = 3(3 + -6x)(4 + -2x)

Multiply (-5 + 10x) * (1 + 2x)
(-5(1 + 2x) + 10x * (1 + 2x)) = 3(3 + -6x)(4 + -2x)
((1 * -5 + 2x * -5) + 10x * (1 + 2x)) = 3(3 + -6x)(4 + -2x)
((-5 + -10x) + 10x * (1 + 2x)) = 3(3 + -6x)(4 + -2x)
(-5 + -10x + (1 * 10x + 2x * 10x)) = 3(3 + -6x)(4 + -2x)
(-5 + -10x + (10x + 20x2)) = 3(3 + -6x)(4 + -2x)

Combine like terms: -10x + 10x = 0
(-5 + 0 + 20x2) = 3(3 + -6x)(4 + -2x)
(-5 + 20x2) = 3(3 + -6x)(4 + -2x)

Multiply (3 + -6x) * (4 + -2x)
-5 + 20x2 = 3(3(4 + -2x) + -6x * (4 + -2x))
-5 + 20x2 = 3((4 * 3 + -2x * 3) + -6x * (4 + -2x))
-5 + 20x2 = 3((12 + -6x) + -6x * (4 + -2x))
-5 + 20x2 = 3(12 + -6x + (4 * -6x + -2x * -6x))
-5 + 20x2 = 3(12 + -6x + (-24x + 12x2))

Combine like terms: -6x + -24x = -30x
-5 + 20x2 = 3(12 + -30x + 12x2)
-5 + 20x2 = (12 * 3 + -30x * 3 + 12x2 * 3)
-5 + 20x2 = (36 + -90x + 36x2)

Solving
-5 + 20x2 = 36 + -90x + 36x2

Solving for variable 'x'.

Reorder the terms:
-5 + -36 + 90x + 20x2 + -36x2 = 36 + -90x + 36x2 + -36 + 90x + -36x2

Combine like terms: -5 + -36 = -41
-41 + 90x + 20x2 + -36x2 = 36 + -90x + 36x2 + -36 + 90x + -36x2

Combine like terms: 20x2 + -36x2 = -16x2
-41 + 90x + -16x2 = 36 + -90x + 36x2 + -36 + 90x + -36x2

Reorder the terms:
-41 + 90x + -16x2 = 36 + -36 + -90x + 90x + 36x2 + -36x2

Combine like terms: 36 + -36 = 0
-41 + 90x + -16x2 = 0 + -90x + 90x + 36x2 + -36x2
-41 + 90x + -16x2 = -90x + 90x + 36x2 + -36x2

Combine like terms: -90x + 90x = 0
-41 + 90x + -16x2 = 0 + 36x2 + -36x2
-41 + 90x + -16x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
-41 + 90x + -16x2 = 0

Factor a trinomial.
(-41 + 8x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-41 + 8x)' equal to zero and attempt to solve:

Simplifying
-41 + 8x = 0

Solving
-41 + 8x = 0

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

Add '41' to each side of the equation.
-41 + 41 + 8x = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 8x = 0 + 41
8x = 0 + 41

Combine like terms: 0 + 41 = 41
8x = 41

Divide each side by '8'.
x = 5.125

Simplifying
x = 5.125

Subproblem 2
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
Solution
x = {5.125, 0.5}

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