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

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


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

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

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

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

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

Solving
-10 + 16x + 8x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

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

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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 0.5}

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