5x^2+19x=5x-8

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Solution for 5x^2+19x=5x-8 equation: 


Simplifying
5x2 + 19x = 5x + -8

Reorder the terms:
19x + 5x2 = 5x + -8

Reorder the terms:
19x + 5x2 = -8 + 5x

Solving
19x + 5x2 = -8 + 5x

Solving for variable 'x'.

Reorder the terms:
8 + 19x + -5x + 5x2 = -8 + 5x + 8 + -5x

Combine like terms: 19x + -5x = 14x
8 + 14x + 5x2 = -8 + 5x + 8 + -5x

Reorder the terms:
8 + 14x + 5x2 = -8 + 8 + 5x + -5x

Combine like terms: -8 + 8 = 0
8 + 14x + 5x2 = 0 + 5x + -5x
8 + 14x + 5x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
8 + 14x + 5x2 = 0

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


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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

Solving
4 + 5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4

Combine like terms: 0 + -4 = -4
5x = -4

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8
Solution
x = {-2, -0.8}

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