15x^2-11x-3=2x+3

Solution for 15x^2-11x-3=2x+3 equation:

Simplifying
15x2 + -11x + -3 = 2x + 3

Reorder the terms:
-3 + -11x + 15x2 = 2x + 3

Reorder the terms:
-3 + -11x + 15x2 = 3 + 2x

Solving
-3 + -11x + 15x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
-3 + -3 + -11x + -2x + 15x2 = 3 + 2x + -3 + -2x

Combine like terms: -3 + -3 = -6
-6 + -11x + -2x + 15x2 = 3 + 2x + -3 + -2x

Combine like terms: -11x + -2x = -13x
-6 + -13x + 15x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-6 + -13x + 15x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-6 + -13x + 15x2 = 0 + 2x + -2x
-6 + -13x + 15x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + -13x + 15x2 = 0

Factor a trinomial.
(-1 + -3x)(6 + -5x) = 0

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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 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 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-0.3333333333, 1.2}