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

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


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

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

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

Multiply (5 + 5x) * (-5 + 4x)
(5(-5 + 4x) + 5x * (-5 + 4x)) = 0
((-5 * 5 + 4x * 5) + 5x * (-5 + 4x)) = 0
((-25 + 20x) + 5x * (-5 + 4x)) = 0
(-25 + 20x + (-5 * 5x + 4x * 5x)) = 0
(-25 + 20x + (-25x + 20x2)) = 0

Combine like terms: 20x + -25x = -5x
(-25 + -5x + 20x2) = 0

Solving
-25 + -5x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + -1x + 4x2) = 0

Factor a trinomial.
5((-1 + -1x)(5 + -4x)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-1, 1.25}

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