19=2x^2+3x+5

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Solution for 19=2x^2+3x+5 equation: 


Simplifying
19 = 2x2 + 3x + 5

Reorder the terms:
19 = 5 + 3x + 2x2

Solving
19 = 5 + 3x + 2x2

Solving for variable 'x'.

Combine like terms: 19 + -5 = 14
14 + -3x + -2x2 = 5 + 3x + 2x2 + -5 + -3x + -2x2

Reorder the terms:
14 + -3x + -2x2 = 5 + -5 + 3x + -3x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
14 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
14 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
14 + -3x + -2x2 = 0 + 2x2 + -2x2
14 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
14 + -3x + -2x2 = 0

Factor a trinomial.
(2 + -1x)(7 + 2x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {2, -3.5}

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