x^2-8x+21=3x-7

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Solution for x^2-8x+21=3x-7 equation: 


Simplifying
x2 + -8x + 21 = 3x + -7

Reorder the terms:
21 + -8x + x2 = 3x + -7

Reorder the terms:
21 + -8x + x2 = -7 + 3x

Solving
21 + -8x + x2 = -7 + 3x

Solving for variable 'x'.

Reorder the terms:
21 + 7 + -8x + -3x + x2 = -7 + 3x + 7 + -3x

Combine like terms: 21 + 7 = 28
28 + -8x + -3x + x2 = -7 + 3x + 7 + -3x

Combine like terms: -8x + -3x = -11x
28 + -11x + x2 = -7 + 3x + 7 + -3x

Reorder the terms:
28 + -11x + x2 = -7 + 7 + 3x + -3x

Combine like terms: -7 + 7 = 0
28 + -11x + x2 = 0 + 3x + -3x
28 + -11x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
28 + -11x + x2 = 0

Factor a trinomial.
(4 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {4, 7}

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