2(4x-1)(x-10)=0

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Solution for 2(4x-1)(x-10)=0 equation: 


Simplifying
2(4x + -1)(x + -10) = 0

Reorder the terms:
2(-1 + 4x)(x + -10) = 0

Reorder the terms:
2(-1 + 4x)(-10 + x) = 0

Multiply (-1 + 4x) * (-10 + x)
2(-1(-10 + x) + 4x * (-10 + x)) = 0
2((-10 * -1 + x * -1) + 4x * (-10 + x)) = 0
2((10 + -1x) + 4x * (-10 + x)) = 0
2(10 + -1x + (-10 * 4x + x * 4x)) = 0
2(10 + -1x + (-40x + 4x2)) = 0

Combine like terms: -1x + -40x = -41x
2(10 + -41x + 4x2) = 0
(10 * 2 + -41x * 2 + 4x2 * 2) = 0
(20 + -82x + 8x2) = 0

Solving
20 + -82x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -41x + 4x2) = 0

Factor a trinomial.
2((1 + -4x)(10 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0.25, 10}

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