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

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


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

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

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

Multiply (-4 + x) * (-5 + 4x)
(-4(-5 + 4x) + x(-5 + 4x)) = 0
((-5 * -4 + 4x * -4) + x(-5 + 4x)) = 0
((20 + -16x) + x(-5 + 4x)) = 0
(20 + -16x + (-5 * x + 4x * x)) = 0
(20 + -16x + (-5x + 4x2)) = 0

Combine like terms: -16x + -5x = -21x
(20 + -21x + 4x2) = 0

Solving
20 + -21x + 4x2 = 0

Solving for variable 'x'.

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


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 '(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 = {1.25, 4}

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