5x^2+13x=2x^2-4x+28

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Solution for 5x^2+13x=2x^2-4x+28 equation: 


Simplifying
5x2 + 13x = 2x2 + -4x + 28

Reorder the terms:
13x + 5x2 = 2x2 + -4x + 28

Reorder the terms:
13x + 5x2 = 28 + -4x + 2x2

Solving
13x + 5x2 = 28 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-28 + 13x + 4x + 5x2 + -2x2 = 28 + -4x + 2x2 + -28 + 4x + -2x2

Combine like terms: 13x + 4x = 17x
-28 + 17x + 5x2 + -2x2 = 28 + -4x + 2x2 + -28 + 4x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-28 + 17x + 3x2 = 28 + -4x + 2x2 + -28 + 4x + -2x2

Reorder the terms:
-28 + 17x + 3x2 = 28 + -28 + -4x + 4x + 2x2 + -2x2

Combine like terms: 28 + -28 = 0
-28 + 17x + 3x2 = 0 + -4x + 4x + 2x2 + -2x2
-28 + 17x + 3x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
-28 + 17x + 3x2 = 0 + 2x2 + -2x2
-28 + 17x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-28 + 17x + 3x2 = 0

Factor a trinomial.
(-7 + -1x)(4 + -3x) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-7, 1.333333333}

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