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

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


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

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

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

Multiply (2 + 5x) * (-4 + 2x)
(2(-4 + 2x) + 5x * (-4 + 2x)) = 0
((-4 * 2 + 2x * 2) + 5x * (-4 + 2x)) = 0
((-8 + 4x) + 5x * (-4 + 2x)) = 0
(-8 + 4x + (-4 * 5x + 2x * 5x)) = 0
(-8 + 4x + (-20x + 10x2)) = 0

Combine like terms: 4x + -20x = -16x
(-8 + -16x + 10x2) = 0

Solving
-8 + -16x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -8x + 5x2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 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 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

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

Simplifying
2 + -1x = 0

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

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.4, 2}

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