2x^2=13x-15

Solution for 2x^2=13x-15 equation:

Simplifying
2x2 = 13x + -15

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

Solving
2x2 = -15 + 13x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(3 + -2x)(5 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1.5, 5}