6x^2-19x=-15

Solution for 6x^2-19x=-15 equation:

Simplifying
6x2 + -19x = -15

Reorder the terms:
-19x + 6x2 = -15

Solving
-19x + 6x2 = -15

Solving for variable 'x'.

Reorder the terms:
15 + -19x + 6x2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -19x + 6x2 = 0

Factor a trinomial.
(3 + -2x)(5 + -3x) = 0

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {1.5, 1.666666667}