3x^2-10x+20=x^2+3x

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Solution for 3x^2-10x+20=x^2+3x equation: 


Simplifying
3x2 + -10x + 20 = x2 + 3x

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

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

Solving
20 + -10x + 3x2 = 3x + x2

Solving for variable 'x'.

Reorder the terms:
20 + -10x + -3x + 3x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: -10x + -3x = -13x
20 + -13x + 3x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
20 + -13x + 2x2 = 3x + x2 + -3x + -1x2

Reorder the terms:
20 + -13x + 2x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
20 + -13x + 2x2 = 0 + x2 + -1x2
20 + -13x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + -13x + 2x2 = 0

Factor a trinomial.
(5 + -2x)(4 + -1x) = 0


Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
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
Solution
x = {2.5, 4}

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