3x^2+4x-13=22-4x

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Solution for 3x^2+4x-13=22-4x equation: 


Simplifying
3x2 + 4x + -13 = 22 + -4x

Reorder the terms:
-13 + 4x + 3x2 = 22 + -4x

Solving
-13 + 4x + 3x2 = 22 + -4x

Solving for variable 'x'.

Reorder the terms:
-13 + -22 + 4x + 4x + 3x2 = 22 + -4x + -22 + 4x

Combine like terms: -13 + -22 = -35
-35 + 4x + 4x + 3x2 = 22 + -4x + -22 + 4x

Combine like terms: 4x + 4x = 8x
-35 + 8x + 3x2 = 22 + -4x + -22 + 4x

Reorder the terms:
-35 + 8x + 3x2 = 22 + -22 + -4x + 4x

Combine like terms: 22 + -22 = 0
-35 + 8x + 3x2 = 0 + -4x + 4x
-35 + 8x + 3x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-35 + 8x + 3x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -3x) = 0


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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-5, 2.333333333}

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