(x+2)(5x+3)=12

Solution for (x+2)(5x+3)=12 equation:

Simplifying
(x + 2)(5x + 3) = 12

Reorder the terms:
(2 + x)(5x + 3) = 12

Reorder the terms:
(2 + x)(3 + 5x) = 12

Multiply (2 + x) * (3 + 5x)
(2(3 + 5x) + x(3 + 5x)) = 12
((3 * 2 + 5x * 2) + x(3 + 5x)) = 12
((6 + 10x) + x(3 + 5x)) = 12
(6 + 10x + (3 * x + 5x * x)) = 12
(6 + 10x + (3x + 5x2)) = 12

Combine like terms: 10x + 3x = 13x
(6 + 13x + 5x2) = 12

Solving
6 + 13x + 5x2 = 12

Solving for variable 'x'.

Reorder the terms:
6 + -12 + 13x + 5x2 = 12 + -12

Combine like terms: 6 + -12 = -6
-6 + 13x + 5x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-6 + 13x + 5x2 = 0

Factor a trinomial.
(-3 + -1x)(2 + -5x) = 0

Subproblem 1
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
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 = {-3, 0.4}