2x^2+24x+53=5x+11

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Solution for 2x^2+24x+53=5x+11 equation: 


Simplifying
2x2 + 24x + 53 = 5x + 11

Reorder the terms:
53 + 24x + 2x2 = 5x + 11

Reorder the terms:
53 + 24x + 2x2 = 11 + 5x

Solving
53 + 24x + 2x2 = 11 + 5x

Solving for variable 'x'.

Reorder the terms:
53 + -11 + 24x + -5x + 2x2 = 11 + 5x + -11 + -5x

Combine like terms: 53 + -11 = 42
42 + 24x + -5x + 2x2 = 11 + 5x + -11 + -5x

Combine like terms: 24x + -5x = 19x
42 + 19x + 2x2 = 11 + 5x + -11 + -5x

Reorder the terms:
42 + 19x + 2x2 = 11 + -11 + 5x + -5x

Combine like terms: 11 + -11 = 0
42 + 19x + 2x2 = 0 + 5x + -5x
42 + 19x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
42 + 19x + 2x2 = 0

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


Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6

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 = {-6, -3.5}

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