4x^2+5x-23=13-2x

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Solution for 4x^2+5x-23=13-2x equation: 


Simplifying
4x2 + 5x + -23 = 13 + -2x

Reorder the terms:
-23 + 5x + 4x2 = 13 + -2x

Solving
-23 + 5x + 4x2 = 13 + -2x

Solving for variable 'x'.

Reorder the terms:
-23 + -13 + 5x + 2x + 4x2 = 13 + -2x + -13 + 2x

Combine like terms: -23 + -13 = -36
-36 + 5x + 2x + 4x2 = 13 + -2x + -13 + 2x

Combine like terms: 5x + 2x = 7x
-36 + 7x + 4x2 = 13 + -2x + -13 + 2x

Reorder the terms:
-36 + 7x + 4x2 = 13 + -13 + -2x + 2x

Combine like terms: 13 + -13 = 0
-36 + 7x + 4x2 = 0 + -2x + 2x
-36 + 7x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-36 + 7x + 4x2 = 0

Factor a trinomial.
(-4 + -1x)(9 + -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 '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-4, 2.25}

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