3x^2-25x+62=x^2-11x+50

Solution for 3x^2-25x+62=x^2-11x+50 equation:

Simplifying
3x2 + -25x + 62 = x2 + -11x + 50

Reorder the terms:
62 + -25x + 3x2 = x2 + -11x + 50

Reorder the terms:
62 + -25x + 3x2 = 50 + -11x + x2

Solving
62 + -25x + 3x2 = 50 + -11x + x2

Solving for variable 'x'.

Reorder the terms:
62 + -50 + -25x + 11x + 3x2 + -1x2 = 50 + -11x + x2 + -50 + 11x + -1x2

Combine like terms: 62 + -50 = 12
12 + -25x + 11x + 3x2 + -1x2 = 50 + -11x + x2 + -50 + 11x + -1x2

Combine like terms: -25x + 11x = -14x
12 + -14x + 3x2 + -1x2 = 50 + -11x + x2 + -50 + 11x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
12 + -14x + 2x2 = 50 + -11x + x2 + -50 + 11x + -1x2

Reorder the terms:
12 + -14x + 2x2 = 50 + -50 + -11x + 11x + x2 + -1x2

Combine like terms: 50 + -50 = 0
12 + -14x + 2x2 = 0 + -11x + 11x + x2 + -1x2
12 + -14x + 2x2 = -11x + 11x + x2 + -1x2

Combine like terms: -11x + 11x = 0
12 + -14x + 2x2 = 0 + x2 + -1x2
12 + -14x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -7x + x2) = 0

Factor a trinomial.
2((1 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1, 6}