(4x+5)(2x+3)=120

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Solution for (4x+5)(2x+3)=120 equation: 


Simplifying
(4x + 5)(2x + 3) = 120

Reorder the terms:
(5 + 4x)(2x + 3) = 120

Reorder the terms:
(5 + 4x)(3 + 2x) = 120

Multiply (5 + 4x) * (3 + 2x)
(5(3 + 2x) + 4x * (3 + 2x)) = 120
((3 * 5 + 2x * 5) + 4x * (3 + 2x)) = 120
((15 + 10x) + 4x * (3 + 2x)) = 120
(15 + 10x + (3 * 4x + 2x * 4x)) = 120
(15 + 10x + (12x + 8x2)) = 120

Combine like terms: 10x + 12x = 22x
(15 + 22x + 8x2) = 120

Solving
15 + 22x + 8x2 = 120

Solving for variable 'x'.

Reorder the terms:
15 + -120 + 22x + 8x2 = 120 + -120

Combine like terms: 15 + -120 = -105
-105 + 22x + 8x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-105 + 22x + 8x2 = 0

Factor a trinomial.
(-21 + -4x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-21 + -4x)' equal to zero and attempt to solve:

Simplifying
-21 + -4x = 0

Solving
-21 + -4x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -4x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -4x = 0 + 21
-4x = 0 + 21

Combine like terms: 0 + 21 = 21
-4x = 21

Divide each side by '-4'.
x = -5.25

Simplifying
x = -5.25

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-5.25, 2.5}

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