2x(3-5x)+3(5-2x)-5(3-x)-3x(4x-2)=

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


Simplifying
2x(3 + -5x) + 3(5 + -2x) + -5(3 + -1x) + -3x(4x + -2) = 0
(3 * 2x + -5x * 2x) + 3(5 + -2x) + -5(3 + -1x) + -3x(4x + -2) = 0
(6x + -10x2) + 3(5 + -2x) + -5(3 + -1x) + -3x(4x + -2) = 0
6x + -10x2 + (5 * 3 + -2x * 3) + -5(3 + -1x) + -3x(4x + -2) = 0
6x + -10x2 + (15 + -6x) + -5(3 + -1x) + -3x(4x + -2) = 0
6x + -10x2 + 15 + -6x + (3 * -5 + -1x * -5) + -3x(4x + -2) = 0
6x + -10x2 + 15 + -6x + (-15 + 5x) + -3x(4x + -2) = 0

Reorder the terms:
6x + -10x2 + 15 + -6x + -15 + 5x + -3x(-2 + 4x) = 0
6x + -10x2 + 15 + -6x + -15 + 5x + (-2 * -3x + 4x * -3x) = 0
6x + -10x2 + 15 + -6x + -15 + 5x + (6x + -12x2) = 0

Reorder the terms:
15 + -15 + 6x + -6x + 5x + 6x + -10x2 + -12x2 = 0

Combine like terms: 15 + -15 = 0
0 + 6x + -6x + 5x + 6x + -10x2 + -12x2 = 0
6x + -6x + 5x + 6x + -10x2 + -12x2 = 0

Combine like terms: 6x + -6x = 0
0 + 5x + 6x + -10x2 + -12x2 = 0
5x + 6x + -10x2 + -12x2 = 0

Combine like terms: 5x + 6x = 11x
11x + -10x2 + -12x2 = 0

Combine like terms: -10x2 + -12x2 = -22x2
11x + -22x2 = 0

Solving
11x + -22x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '11x'.
11x(1 + -2x) = 0

Ignore the factor 11.

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 '(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 = {0, 0.5}

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