0=3x^2-45x+42

Solution for 0=3x^2-45x+42 equation:

Simplifying
0 = 3x2 + -45x + 42

Reorder the terms:
0 = 42 + -45x + 3x2

Solving
0 = 42 + -45x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -42 = -42
-42 + 45x + -3x2 = 42 + -45x + 3x2 + -42 + 45x + -3x2

Reorder the terms:
-42 + 45x + -3x2 = 42 + -42 + -45x + 45x + 3x2 + -3x2

Combine like terms: 42 + -42 = 0
-42 + 45x + -3x2 = 0 + -45x + 45x + 3x2 + -3x2
-42 + 45x + -3x2 = -45x + 45x + 3x2 + -3x2

Combine like terms: -45x + 45x = 0
-42 + 45x + -3x2 = 0 + 3x2 + -3x2
-42 + 45x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-42 + 45x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 15x + -1x2) = 0

Factor a trinomial.
3((-14 + x)(1 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-14 + x)' equal to zero and attempt to solve:

Simplifying
-14 + x = 0

Solving
-14 + x = 0

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

Add '14' to each side of the equation.
-14 + 14 + x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + x = 0 + 14
x = 0 + 14

Combine like terms: 0 + 14 = 14
x = 14

Simplifying
x = 14
Subproblem 2
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
Solution
x = {14, 1}