(4x+1)(4-5x)=0

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Solution for (4x+1)(4-5x)=0 equation: 


Simplifying
(4x + 1)(4 + -5x) = 0

Reorder the terms:
(1 + 4x)(4 + -5x) = 0

Multiply (1 + 4x) * (4 + -5x)
(1(4 + -5x) + 4x * (4 + -5x)) = 0
((4 * 1 + -5x * 1) + 4x * (4 + -5x)) = 0
((4 + -5x) + 4x * (4 + -5x)) = 0
(4 + -5x + (4 * 4x + -5x * 4x)) = 0
(4 + -5x + (16x + -20x2)) = 0

Combine like terms: -5x + 16x = 11x
(4 + 11x + -20x2) = 0

Solving
4 + 11x + -20x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8

Subproblem 2
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
Solution
x = {0.8, -0.25}

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