5x^2=37x-42

Solution for 5x^2=37x-42 equation:

Simplifying
5x2 = 37x + -42

Reorder the terms:
5x2 = -42 + 37x

Solving
5x2 = -42 + 37x

Solving for variable 'x'.

Reorder the terms:
42 + -37x + 5x2 = -42 + 37x + 42 + -37x

Reorder the terms:
42 + -37x + 5x2 = -42 + 42 + 37x + -37x

Combine like terms: -42 + 42 = 0
42 + -37x + 5x2 = 0 + 37x + -37x
42 + -37x + 5x2 = 37x + -37x

Combine like terms: 37x + -37x = 0
42 + -37x + 5x2 = 0

Factor a trinomial.
(7 + -5x)(6 + -1x) = 0

Subproblem 1
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 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 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
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 = {1.4, 6}