4x^2+3x-23=5-6x

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Solution for 4x^2+3x-23=5-6x equation: 


Simplifying
4x2 + 3x + -23 = 5 + -6x

Reorder the terms:
-23 + 3x + 4x2 = 5 + -6x

Solving
-23 + 3x + 4x2 = 5 + -6x

Solving for variable 'x'.

Reorder the terms:
-23 + -5 + 3x + 6x + 4x2 = 5 + -6x + -5 + 6x

Combine like terms: -23 + -5 = -28
-28 + 3x + 6x + 4x2 = 5 + -6x + -5 + 6x

Combine like terms: 3x + 6x = 9x
-28 + 9x + 4x2 = 5 + -6x + -5 + 6x

Reorder the terms:
-28 + 9x + 4x2 = 5 + -5 + -6x + 6x

Combine like terms: 5 + -5 = 0
-28 + 9x + 4x2 = 0 + -6x + 6x
-28 + 9x + 4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-28 + 9x + 4x2 = 0

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


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 1.75}

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