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

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


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

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