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

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


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

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

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

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

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

Solving
-20 + 10x + 10x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
10((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 10.

Subproblem 1
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

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

Simplifying
1 + -1x = 0

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

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

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

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

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

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