5x(2-x)+4x(2x-5)-(3x-4)=0

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Solution for 5x(2-x)+4x(2x-5)-(3x-4)=0 equation: 


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

Reorder the terms:
10x + -5x2 + 4x(-5 + 2x) + -1(3x + -4) = 0
10x + -5x2 + (-5 * 4x + 2x * 4x) + -1(3x + -4) = 0
10x + -5x2 + (-20x + 8x2) + -1(3x + -4) = 0

Reorder the terms:
10x + -5x2 + -20x + 8x2 + -1(-4 + 3x) = 0
10x + -5x2 + -20x + 8x2 + (-4 * -1 + 3x * -1) = 0
10x + -5x2 + -20x + 8x2 + (4 + -3x) = 0

Reorder the terms:
4 + 10x + -20x + -3x + -5x2 + 8x2 = 0

Combine like terms: 10x + -20x = -10x
4 + -10x + -3x + -5x2 + 8x2 = 0

Combine like terms: -10x + -3x = -13x
4 + -13x + -5x2 + 8x2 = 0

Combine like terms: -5x2 + 8x2 = 3x2
4 + -13x + 3x2 = 0

Solving
4 + -13x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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 = {0.3333333333, 4}

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