4x(x-2)-5x(x-1)-2=0

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Solution for 4x(x-2)-5x(x-1)-2=0 equation: 


Simplifying
4x(x + -2) + -5x(x + -1) + -2 = 0

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

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

Reorder the terms:
-2 + -8x + 5x + 4x2 + -5x2 = 0

Combine like terms: -8x + 5x = -3x
-2 + -3x + 4x2 + -5x2 = 0

Combine like terms: 4x2 + -5x2 = -1x2
-2 + -3x + -1x2 = 0

Solving
-2 + -3x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 3x + x2) = 0

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

Ignore the factor -1.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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