(5x+1)(4x+3)=80x

Solution for (5x+1)(4x+3)=80x equation:

Simplifying
(5x + 1)(4x + 3) = 80x

Reorder the terms:
(1 + 5x)(4x + 3) = 80x

Reorder the terms:
(1 + 5x)(3 + 4x) = 80x

Multiply (1 + 5x) * (3 + 4x)
(1(3 + 4x) + 5x * (3 + 4x)) = 80x
((3 * 1 + 4x * 1) + 5x * (3 + 4x)) = 80x
((3 + 4x) + 5x * (3 + 4x)) = 80x
(3 + 4x + (3 * 5x + 4x * 5x)) = 80x
(3 + 4x + (15x + 20x2)) = 80x

Combine like terms: 4x + 15x = 19x
(3 + 19x + 20x2) = 80x

Solving
3 + 19x + 20x2 = 80x

Solving for variable 'x'.

Reorder the terms:
3 + 19x + -80x + 20x2 = 80x + -80x

Combine like terms: 19x + -80x = -61x
3 + -61x + 20x2 = 80x + -80x

Combine like terms: 80x + -80x = 0
3 + -61x + 20x2 = 0

Factor a trinomial.
(1 + -20x)(3 + -1x) = 0

Subproblem 1
Set the factor '(1 + -20x)' equal to zero and attempt to solve:

Simplifying
1 + -20x = 0

Solving
1 + -20x = 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 + -20x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -20x = 0 + -1
-20x = 0 + -1

Combine like terms: 0 + -1 = -1
-20x = -1

Divide each side by '-20'.
x = 0.05

Simplifying
x = 0.05
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 = {0.05, 3}