x^2-6x+9=2x^2-10x+4

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Solution for x^2-6x+9=2x^2-10x+4 equation: 


Simplifying
x2 + -6x + 9 = 2x2 + -10x + 4

Reorder the terms:
9 + -6x + x2 = 2x2 + -10x + 4

Reorder the terms:
9 + -6x + x2 = 4 + -10x + 2x2

Solving
9 + -6x + x2 = 4 + -10x + 2x2

Solving for variable 'x'.

Reorder the terms:
9 + -4 + -6x + 10x + x2 + -2x2 = 4 + -10x + 2x2 + -4 + 10x + -2x2

Combine like terms: 9 + -4 = 5
5 + -6x + 10x + x2 + -2x2 = 4 + -10x + 2x2 + -4 + 10x + -2x2

Combine like terms: -6x + 10x = 4x
5 + 4x + x2 + -2x2 = 4 + -10x + 2x2 + -4 + 10x + -2x2

Combine like terms: x2 + -2x2 = -1x2
5 + 4x + -1x2 = 4 + -10x + 2x2 + -4 + 10x + -2x2

Reorder the terms:
5 + 4x + -1x2 = 4 + -4 + -10x + 10x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
5 + 4x + -1x2 = 0 + -10x + 10x + 2x2 + -2x2
5 + 4x + -1x2 = -10x + 10x + 2x2 + -2x2

Combine like terms: -10x + 10x = 0
5 + 4x + -1x2 = 0 + 2x2 + -2x2
5 + 4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 4x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(1 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {5, -1}

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