4x^2+22x-19=5-7x

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Solution for 4x^2+22x-19=5-7x equation: 


Simplifying
4x2 + 22x + -19 = 5 + -7x

Reorder the terms:
-19 + 22x + 4x2 = 5 + -7x

Solving
-19 + 22x + 4x2 = 5 + -7x

Solving for variable 'x'.

Reorder the terms:
-19 + -5 + 22x + 7x + 4x2 = 5 + -7x + -5 + 7x

Combine like terms: -19 + -5 = -24
-24 + 22x + 7x + 4x2 = 5 + -7x + -5 + 7x

Combine like terms: 22x + 7x = 29x
-24 + 29x + 4x2 = 5 + -7x + -5 + 7x

Reorder the terms:
-24 + 29x + 4x2 = 5 + -5 + -7x + 7x

Combine like terms: 5 + -5 = 0
-24 + 29x + 4x2 = 0 + -7x + 7x
-24 + 29x + 4x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-24 + 29x + 4x2 = 0

Factor a trinomial.
(-8 + -1x)(3 + -4x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-8, 0.75}

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