(4x+36)(8x-40)=0

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Solution for (4x+36)(8x-40)=0 equation: 


Simplifying
(4x + 36)(8x + -40) = 0

Reorder the terms:
(36 + 4x)(8x + -40) = 0

Reorder the terms:
(36 + 4x)(-40 + 8x) = 0

Multiply (36 + 4x) * (-40 + 8x)
(36(-40 + 8x) + 4x * (-40 + 8x)) = 0
((-40 * 36 + 8x * 36) + 4x * (-40 + 8x)) = 0
((-1440 + 288x) + 4x * (-40 + 8x)) = 0
(-1440 + 288x + (-40 * 4x + 8x * 4x)) = 0
(-1440 + 288x + (-160x + 32x2)) = 0

Combine like terms: 288x + -160x = 128x
(-1440 + 128x + 32x2) = 0

Solving
-1440 + 128x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '32'.
32(-45 + 4x + x2) = 0

Factor a trinomial.
32((-9 + -1x)(5 + -1x)) = 0

Ignore the factor 32.

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-9, 5}

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