0=5x^2-23x-10

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Solution for 0=5x^2-23x-10 equation: 


Simplifying
0 = 5x2 + -23x + -10

Reorder the terms:
0 = -10 + -23x + 5x2

Solving
0 = -10 + -23x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 10 = 10
10 + 23x + -5x2 = -10 + -23x + 5x2 + 10 + 23x + -5x2

Reorder the terms:
10 + 23x + -5x2 = -10 + 10 + -23x + 23x + 5x2 + -5x2

Combine like terms: -10 + 10 = 0
10 + 23x + -5x2 = 0 + -23x + 23x + 5x2 + -5x2
10 + 23x + -5x2 = -23x + 23x + 5x2 + -5x2

Combine like terms: -23x + 23x = 0
10 + 23x + -5x2 = 0 + 5x2 + -5x2
10 + 23x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
10 + 23x + -5x2 = 0

Factor a trinomial.
(5 + -1x)(2 + 5x) = 0


Subproblem 1
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

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

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

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

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

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {5, -0.4}

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