0=24x^2+100x+100

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Solution for 0=24x^2+100x+100 equation: 


Simplifying
0 = 24x2 + 100x + 100

Reorder the terms:
0 = 100 + 100x + 24x2

Solving
0 = 100 + 100x + 24x2

Solving for variable 'x'.

Combine like terms: 0 + -100 = -100
-100 + -100x + -24x2 = 100 + 100x + 24x2 + -100 + -100x + -24x2

Reorder the terms:
-100 + -100x + -24x2 = 100 + -100 + 100x + -100x + 24x2 + -24x2

Combine like terms: 100 + -100 = 0
-100 + -100x + -24x2 = 0 + 100x + -100x + 24x2 + -24x2
-100 + -100x + -24x2 = 100x + -100x + 24x2 + -24x2

Combine like terms: 100x + -100x = 0
-100 + -100x + -24x2 = 0 + 24x2 + -24x2
-100 + -100x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
-100 + -100x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(25 + 25x + 6x2) = 0

Factor a trinomial.
-4((5 + 2x)(5 + 3x)) = 0

Ignore the factor -4.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {-2.5, -1.666666667}

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