(4x-10)(24+5x)=0

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Solution for (4x-10)(24+5x)=0 equation: 


Simplifying
(4x + -10)(24 + 5x) = 0

Reorder the terms:
(-10 + 4x)(24 + 5x) = 0

Multiply (-10 + 4x) * (24 + 5x)
(-10(24 + 5x) + 4x * (24 + 5x)) = 0
((24 * -10 + 5x * -10) + 4x * (24 + 5x)) = 0
((-240 + -50x) + 4x * (24 + 5x)) = 0
(-240 + -50x + (24 * 4x + 5x * 4x)) = 0
(-240 + -50x + (96x + 20x2)) = 0

Combine like terms: -50x + 96x = 46x
(-240 + 46x + 20x2) = 0

Solving
-240 + 46x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + 23x + 10x2) = 0

Factor a trinomial.
2((-24 + -5x)(5 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + -5x)' equal to zero and attempt to solve:

Simplifying
-24 + -5x = 0

Solving
-24 + -5x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -5x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -5x = 0 + 24
-5x = 0 + 24

Combine like terms: 0 + 24 = 24
-5x = 24

Divide each side by '-5'.
x = -4.8

Simplifying
x = -4.8

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-4.8, 2.5}

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