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

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


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

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

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

Solving for variable 'x'.

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

Combine like terms: -19 + -23 = -42
-42 + 13x + 4x + 4x2 = 23 + -4x + -23 + 4x

Combine like terms: 13x + 4x = 17x
-42 + 17x + 4x2 = 23 + -4x + -23 + 4x

Reorder the terms:
-42 + 17x + 4x2 = 23 + -23 + -4x + 4x

Combine like terms: 23 + -23 = 0
-42 + 17x + 4x2 = 0 + -4x + 4x
-42 + 17x + 4x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-42 + 17x + 4x2 = 0

Factor a trinomial.
(-6 + -1x)(7 + -4x) = 0


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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-6, 1.75}

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