0=9x^2-61x+42

Solution for 0=9x^2-61x+42 equation:

Simplifying
0 = 9x2 + -61x + 42

Reorder the terms:
0 = 42 + -61x + 9x2

Solving
0 = 42 + -61x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -42 = -42
-42 + 61x + -9x2 = 42 + -61x + 9x2 + -42 + 61x + -9x2

Reorder the terms:
-42 + 61x + -9x2 = 42 + -42 + -61x + 61x + 9x2 + -9x2

Combine like terms: 42 + -42 = 0
-42 + 61x + -9x2 = 0 + -61x + 61x + 9x2 + -9x2
-42 + 61x + -9x2 = -61x + 61x + 9x2 + -9x2

Combine like terms: -61x + 61x = 0
-42 + 61x + -9x2 = 0 + 9x2 + -9x2
-42 + 61x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-42 + 61x + -9x2 = 0

Factor a trinomial.
(-6 + x)(7 + -9x) = 0

Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

Simplifying
x = 6
Subproblem 2
Set the factor '(7 + -9x)' equal to zero and attempt to solve:

Simplifying
7 + -9x = 0

Solving
7 + -9x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -9x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9x = 0 + -7
-9x = 0 + -7

Combine like terms: 0 + -7 = -7
-9x = -7

Divide each side by '-9'.
x = 0.7777777778

Simplifying
x = 0.7777777778
Solution
x = {6, 0.7777777778}