(3x+5)(4x+3)=2x

Solution for (3x+5)(4x+3)=2x equation:

Simplifying
(3x + 5)(4x + 3) = 2x

Reorder the terms:
(5 + 3x)(4x + 3) = 2x

Reorder the terms:
(5 + 3x)(3 + 4x) = 2x

Multiply (5 + 3x) * (3 + 4x)
(5(3 + 4x) + 3x * (3 + 4x)) = 2x
((3 * 5 + 4x * 5) + 3x * (3 + 4x)) = 2x
((15 + 20x) + 3x * (3 + 4x)) = 2x
(15 + 20x + (3 * 3x + 4x * 3x)) = 2x
(15 + 20x + (9x + 12x2)) = 2x

Combine like terms: 20x + 9x = 29x
(15 + 29x + 12x2) = 2x

Solving
15 + 29x + 12x2 = 2x

Solving for variable 'x'.

Reorder the terms:
15 + 29x + -2x + 12x2 = 2x + -2x

Combine like terms: 29x + -2x = 27x
15 + 27x + 12x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
15 + 27x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 9x + 4x2) = 0

Factor a trinomial.
3((5 + 4x)(1 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 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 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-1.25, -1}