10x^2+13x=2x+6

Solution for 10x^2+13x=2x+6 equation:

Simplifying
10x2 + 13x = 2x + 6

Reorder the terms:
13x + 10x2 = 2x + 6

Reorder the terms:
13x + 10x2 = 6 + 2x

Solving
13x + 10x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
-6 + 13x + -2x + 10x2 = 6 + 2x + -6 + -2x

Combine like terms: 13x + -2x = 11x
-6 + 11x + 10x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-6 + 11x + 10x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-6 + 11x + 10x2 = 0 + 2x + -2x
-6 + 11x + 10x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + 11x + 10x2 = 0

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-1.5, 0.4}