2x+10=2x^2+19x+45

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Solution for 2x+10=2x^2+19x+45 equation: 


Simplifying
2x + 10 = 2x2 + 19x + 45

Reorder the terms:
10 + 2x = 2x2 + 19x + 45

Reorder the terms:
10 + 2x = 45 + 19x + 2x2

Solving
10 + 2x = 45 + 19x + 2x2

Solving for variable 'x'.

Reorder the terms:
10 + -45 + 2x + -19x + -2x2 = 45 + 19x + 2x2 + -45 + -19x + -2x2

Combine like terms: 10 + -45 = -35
-35 + 2x + -19x + -2x2 = 45 + 19x + 2x2 + -45 + -19x + -2x2

Combine like terms: 2x + -19x = -17x
-35 + -17x + -2x2 = 45 + 19x + 2x2 + -45 + -19x + -2x2

Reorder the terms:
-35 + -17x + -2x2 = 45 + -45 + 19x + -19x + 2x2 + -2x2

Combine like terms: 45 + -45 = 0
-35 + -17x + -2x2 = 0 + 19x + -19x + 2x2 + -2x2
-35 + -17x + -2x2 = 19x + -19x + 2x2 + -2x2

Combine like terms: 19x + -19x = 0
-35 + -17x + -2x2 = 0 + 2x2 + -2x2
-35 + -17x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-35 + -17x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 17x + 2x2) = 0

Factor a trinomial.
-1((5 + x)(7 + 2x)) = 0

Ignore the factor -1.

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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5

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 = {-5, -3.5}

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