4x(x+8)-5(x+8)=0

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Solution for 4x(x+8)-5(x+8)=0 equation: 


Simplifying
4x(x + 8) + -5(x + 8) = 0

Reorder the terms:
4x(8 + x) + -5(x + 8) = 0
(8 * 4x + x * 4x) + -5(x + 8) = 0
(32x + 4x2) + -5(x + 8) = 0

Reorder the terms:
32x + 4x2 + -5(8 + x) = 0
32x + 4x2 + (8 * -5 + x * -5) = 0
32x + 4x2 + (-40 + -5x) = 0

Reorder the terms:
-40 + 32x + -5x + 4x2 = 0

Combine like terms: 32x + -5x = 27x
-40 + 27x + 4x2 = 0

Solving
-40 + 27x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -1x)(5 + -4x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
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
Solution
x = {-8, 1.25}

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