5x^2-10x+20=4x^2-2x+5

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Solution for 5x^2-10x+20=4x^2-2x+5 equation: 


Simplifying
5x2 + -10x + 20 = 4x2 + -2x + 5

Reorder the terms:
20 + -10x + 5x2 = 4x2 + -2x + 5

Reorder the terms:
20 + -10x + 5x2 = 5 + -2x + 4x2

Solving
20 + -10x + 5x2 = 5 + -2x + 4x2

Solving for variable 'x'.

Reorder the terms:
20 + -5 + -10x + 2x + 5x2 + -4x2 = 5 + -2x + 4x2 + -5 + 2x + -4x2

Combine like terms: 20 + -5 = 15
15 + -10x + 2x + 5x2 + -4x2 = 5 + -2x + 4x2 + -5 + 2x + -4x2

Combine like terms: -10x + 2x = -8x
15 + -8x + 5x2 + -4x2 = 5 + -2x + 4x2 + -5 + 2x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
15 + -8x + 1x2 = 5 + -2x + 4x2 + -5 + 2x + -4x2

Reorder the terms:
15 + -8x + 1x2 = 5 + -5 + -2x + 2x + 4x2 + -4x2

Combine like terms: 5 + -5 = 0
15 + -8x + 1x2 = 0 + -2x + 2x + 4x2 + -4x2
15 + -8x + 1x2 = -2x + 2x + 4x2 + -4x2

Combine like terms: -2x + 2x = 0
15 + -8x + 1x2 = 0 + 4x2 + -4x2
15 + -8x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
15 + -8x + 1x2 = 0

Factor a trinomial.
(3 + -1x)(5 + -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 '(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
Solution
x = {3, 5}

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