x^2-7x+4=3x-20

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Solution for x^2-7x+4=3x-20 equation: 


Simplifying
x2 + -7x + 4 = 3x + -20

Reorder the terms:
4 + -7x + x2 = 3x + -20

Reorder the terms:
4 + -7x + x2 = -20 + 3x

Solving
4 + -7x + x2 = -20 + 3x

Solving for variable 'x'.

Reorder the terms:
4 + 20 + -7x + -3x + x2 = -20 + 3x + 20 + -3x

Combine like terms: 4 + 20 = 24
24 + -7x + -3x + x2 = -20 + 3x + 20 + -3x

Combine like terms: -7x + -3x = -10x
24 + -10x + x2 = -20 + 3x + 20 + -3x

Reorder the terms:
24 + -10x + x2 = -20 + 20 + 3x + -3x

Combine like terms: -20 + 20 = 0
24 + -10x + x2 = 0 + 3x + -3x
24 + -10x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
24 + -10x + x2 = 0

Factor a trinomial.
(4 + -1x)(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}

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