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

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

Simplifying
0 = (5x + -2)(x + 3)

Reorder the terms:
0 = (-2 + 5x)(x + 3)

Reorder the terms:
0 = (-2 + 5x)(3 + x)

Multiply (-2 + 5x) * (3 + x)
0 = (-2(3 + x) + 5x * (3 + x))
0 = ((3 * -2 + x * -2) + 5x * (3 + x))
0 = ((-6 + -2x) + 5x * (3 + x))
0 = (-6 + -2x + (3 * 5x + x * 5x))
0 = (-6 + -2x + (15x + 5x2))

Combine like terms: -2x + 15x = 13x
0 = (-6 + 13x + 5x2)

Solving
0 = -6 + 13x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -13x + -5x2 = -6 + 13x + 5x2 + 6 + -13x + -5x2

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

Combine like terms: -6 + 6 = 0
6 + -13x + -5x2 = 0 + 13x + -13x + 5x2 + -5x2
6 + -13x + -5x2 = 13x + -13x + 5x2 + -5x2

Combine like terms: 13x + -13x = 0
6 + -13x + -5x2 = 0 + 5x2 + -5x2
6 + -13x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
6 + -13x + -5x2 = 0

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

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {0.4, -3}