5x-9=x^2-3x+7

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Solution for 5x-9=x^2-3x+7 equation: 


Simplifying
5x + -9 = x2 + -3x + 7

Reorder the terms:
-9 + 5x = x2 + -3x + 7

Reorder the terms:
-9 + 5x = 7 + -3x + x2

Solving
-9 + 5x = 7 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
-9 + -7 + 5x + 3x + -1x2 = 7 + -3x + x2 + -7 + 3x + -1x2

Combine like terms: -9 + -7 = -16
-16 + 5x + 3x + -1x2 = 7 + -3x + x2 + -7 + 3x + -1x2

Combine like terms: 5x + 3x = 8x
-16 + 8x + -1x2 = 7 + -3x + x2 + -7 + 3x + -1x2

Reorder the terms:
-16 + 8x + -1x2 = 7 + -7 + -3x + 3x + x2 + -1x2

Combine like terms: 7 + -7 = 0
-16 + 8x + -1x2 = 0 + -3x + 3x + x2 + -1x2
-16 + 8x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
-16 + 8x + -1x2 = 0 + x2 + -1x2
-16 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 + 8x + -1x2 = 0

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


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

Simplifying
-4 + x = 0

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

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

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

Simplifying
x = 4

Subproblem 2
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
Solution
x = {4, 4}

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