(4x-5)*(2x-10)=0

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Solution for (4x-5)*(2x-10)=0 equation: 


Simplifying
(4x + -5)(2x + -10) = 0

Reorder the terms:
(-5 + 4x)(2x + -10) = 0

Reorder the terms:
(-5 + 4x)(-10 + 2x) = 0

Multiply (-5 + 4x) * (-10 + 2x)
(-5(-10 + 2x) + 4x * (-10 + 2x)) = 0
((-10 * -5 + 2x * -5) + 4x * (-10 + 2x)) = 0
((50 + -10x) + 4x * (-10 + 2x)) = 0
(50 + -10x + (-10 * 4x + 2x * 4x)) = 0
(50 + -10x + (-40x + 8x2)) = 0

Combine like terms: -10x + -40x = -50x
(50 + -50x + 8x2) = 0

Solving
50 + -50x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -25x + 4x2) = 0

Factor a trinomial.
2((5 + -4x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
5 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1.25, 5}

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