5x^2+23x+1=4x^2+28x-5

Solution for 5x^2+23x+1=4x^2+28x-5 equation:

Simplifying
5x2 + 23x + 1 = 4x2 + 28x + -5

Reorder the terms:
1 + 23x + 5x2 = 4x2 + 28x + -5

Reorder the terms:
1 + 23x + 5x2 = -5 + 28x + 4x2

Solving
1 + 23x + 5x2 = -5 + 28x + 4x2

Solving for variable 'x'.

Reorder the terms:
1 + 5 + 23x + -28x + 5x2 + -4x2 = -5 + 28x + 4x2 + 5 + -28x + -4x2

Combine like terms: 1 + 5 = 6
6 + 23x + -28x + 5x2 + -4x2 = -5 + 28x + 4x2 + 5 + -28x + -4x2

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

Combine like terms: 5x2 + -4x2 = 1x2
6 + -5x + 1x2 = -5 + 28x + 4x2 + 5 + -28x + -4x2

Reorder the terms:
6 + -5x + 1x2 = -5 + 5 + 28x + -28x + 4x2 + -4x2

Combine like terms: -5 + 5 = 0
6 + -5x + 1x2 = 0 + 28x + -28x + 4x2 + -4x2
6 + -5x + 1x2 = 28x + -28x + 4x2 + -4x2

Combine like terms: 28x + -28x = 0
6 + -5x + 1x2 = 0 + 4x2 + -4x2
6 + -5x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -5x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}