3x^2-19x+40=x^2-11x+50

Solution for 3x^2-19x+40=x^2-11x+50 equation:

Simplifying
3x2 + -19x + 40 = x2 + -11x + 50

Reorder the terms:
40 + -19x + 3x2 = x2 + -11x + 50

Reorder the terms:
40 + -19x + 3x2 = 50 + -11x + x2

Solving
40 + -19x + 3x2 = 50 + -11x + x2

Solving for variable 'x'.

Reorder the terms:
40 + -50 + -19x + 11x + 3x2 + -1x2 = 50 + -11x + x2 + -50 + 11x + -1x2

Combine like terms: 40 + -50 = -10
-10 + -19x + 11x + 3x2 + -1x2 = 50 + -11x + x2 + -50 + 11x + -1x2

Combine like terms: -19x + 11x = -8x
-10 + -8x + 3x2 + -1x2 = 50 + -11x + x2 + -50 + 11x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-10 + -8x + 2x2 = 50 + -11x + x2 + -50 + 11x + -1x2

Reorder the terms:
-10 + -8x + 2x2 = 50 + -50 + -11x + 11x + x2 + -1x2

Combine like terms: 50 + -50 = 0
-10 + -8x + 2x2 = 0 + -11x + 11x + x2 + -1x2
-10 + -8x + 2x2 = -11x + 11x + x2 + -1x2

Combine like terms: -11x + 11x = 0
-10 + -8x + 2x2 = 0 + x2 + -1x2
-10 + -8x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4x + x2) = 0

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

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

Simplifying
-1 + -1x = 0

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

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

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

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

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