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

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


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

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

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

Multiply (-1 + 5x) * (2 + 4x)
(-1(2 + 4x) + 5x * (2 + 4x)) = 0
((2 * -1 + 4x * -1) + 5x * (2 + 4x)) = 0
((-2 + -4x) + 5x * (2 + 4x)) = 0
(-2 + -4x + (2 * 5x + 4x * 5x)) = 0
(-2 + -4x + (10x + 20x2)) = 0

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

Solving
-2 + 6x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 3x + 10x2) = 0

Factor a trinomial.
2((-1 + -2x)(1 + -5x)) = 0

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-0.5, 0.2}

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