3x^2+19x-13=23-4x

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Solution for 3x^2+19x-13=23-4x equation: 


Simplifying
3x2 + 19x + -13 = 23 + -4x

Reorder the terms:
-13 + 19x + 3x2 = 23 + -4x

Solving
-13 + 19x + 3x2 = 23 + -4x

Solving for variable 'x'.

Reorder the terms:
-13 + -23 + 19x + 4x + 3x2 = 23 + -4x + -23 + 4x

Combine like terms: -13 + -23 = -36
-36 + 19x + 4x + 3x2 = 23 + -4x + -23 + 4x

Combine like terms: 19x + 4x = 23x
-36 + 23x + 3x2 = 23 + -4x + -23 + 4x

Reorder the terms:
-36 + 23x + 3x2 = 23 + -23 + -4x + 4x

Combine like terms: 23 + -23 = 0
-36 + 23x + 3x2 = 0 + -4x + 4x
-36 + 23x + 3x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-36 + 23x + 3x2 = 0

Factor a trinomial.
(-9 + -1x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 1.333333333}

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