x*x-20x+34=-7x+4

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Solution for x*x-20x+34=-7x+4 equation: 


Simplifying
x * x + -20x + 34 = -7x + 4

Multiply x * x
x2 + -20x + 34 = -7x + 4

Reorder the terms:
34 + -20x + x2 = -7x + 4

Reorder the terms:
34 + -20x + x2 = 4 + -7x

Solving
34 + -20x + x2 = 4 + -7x

Solving for variable 'x'.

Reorder the terms:
34 + -4 + -20x + 7x + x2 = 4 + -7x + -4 + 7x

Combine like terms: 34 + -4 = 30
30 + -20x + 7x + x2 = 4 + -7x + -4 + 7x

Combine like terms: -20x + 7x = -13x
30 + -13x + x2 = 4 + -7x + -4 + 7x

Reorder the terms:
30 + -13x + x2 = 4 + -4 + -7x + 7x

Combine like terms: 4 + -4 = 0
30 + -13x + x2 = 0 + -7x + 7x
30 + -13x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
30 + -13x + x2 = 0

Factor a trinomial.
(3 + -1x)(10 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {3, 10}

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