2x^2+13x=2x+21

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Solution for 2x^2+13x=2x+21 equation: 


Simplifying
2x2 + 13x = 2x + 21

Reorder the terms:
13x + 2x2 = 2x + 21

Reorder the terms:
13x + 2x2 = 21 + 2x

Solving
13x + 2x2 = 21 + 2x

Solving for variable 'x'.

Reorder the terms:
-21 + 13x + -2x + 2x2 = 21 + 2x + -21 + -2x

Combine like terms: 13x + -2x = 11x
-21 + 11x + 2x2 = 21 + 2x + -21 + -2x

Reorder the terms:
-21 + 11x + 2x2 = 21 + -21 + 2x + -2x

Combine like terms: 21 + -21 = 0
-21 + 11x + 2x2 = 0 + 2x + -2x
-21 + 11x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-21 + 11x + 2x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-7, 1.5}

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