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

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


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

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

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

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

Combine like terms: -2x + -40x = -42x
(8 + -42x + 10x2) = 0

Solving
8 + -42x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -21x + 5x2) = 0

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

Ignore the factor 2.

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

Simplifying
1 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.2, 4}

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