(2x-5)(3x+1)=10

Solution for (2x-5)(3x+1)=10 equation:

Simplifying
(2x + -5)(3x + 1) = 10

Reorder the terms:
(-5 + 2x)(3x + 1) = 10

Reorder the terms:
(-5 + 2x)(1 + 3x) = 10

Multiply (-5 + 2x) * (1 + 3x)
(-5(1 + 3x) + 2x * (1 + 3x)) = 10
((1 * -5 + 3x * -5) + 2x * (1 + 3x)) = 10
((-5 + -15x) + 2x * (1 + 3x)) = 10
(-5 + -15x + (1 * 2x + 3x * 2x)) = 10
(-5 + -15x + (2x + 6x2)) = 10

Combine like terms: -15x + 2x = -13x
(-5 + -13x + 6x2) = 10

Solving
-5 + -13x + 6x2 = 10

Solving for variable 'x'.

Reorder the terms:
-5 + -10 + -13x + 6x2 = 10 + -10

Combine like terms: -5 + -10 = -15
-15 + -13x + 6x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-15 + -13x + 6x2 = 0

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

Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

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

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

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

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.8333333333, 3}