-6x^2=37x+6

Solution for -6x^2=37x+6 equation:

Simplifying
-6x2 = 37x + 6

Reorder the terms:
-6x2 = 6 + 37x

Solving
-6x2 = 6 + 37x

Solving for variable 'x'.

Reorder the terms:
-6 + -37x + -6x2 = 6 + 37x + -6 + -37x

Reorder the terms:
-6 + -37x + -6x2 = 6 + -6 + 37x + -37x

Combine like terms: 6 + -6 = 0
-6 + -37x + -6x2 = 0 + 37x + -37x
-6 + -37x + -6x2 = 37x + -37x

Combine like terms: 37x + -37x = 0
-6 + -37x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 37x + 6x2) = 0

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

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

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

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

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

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Solution
x = {-6, -0.1666666667}