(x+3)*(4x+5)=65

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Solution for (x+3)*(4x+5)=65 equation: 


Simplifying
(x + 3)(4x + 5) = 65

Reorder the terms:
(3 + x)(4x + 5) = 65

Reorder the terms:
(3 + x)(5 + 4x) = 65

Multiply (3 + x) * (5 + 4x)
(3(5 + 4x) + x(5 + 4x)) = 65
((5 * 3 + 4x * 3) + x(5 + 4x)) = 65
((15 + 12x) + x(5 + 4x)) = 65
(15 + 12x + (5 * x + 4x * x)) = 65
(15 + 12x + (5x + 4x2)) = 65

Combine like terms: 12x + 5x = 17x
(15 + 17x + 4x2) = 65

Solving
15 + 17x + 4x2 = 65

Solving for variable 'x'.

Reorder the terms:
15 + -65 + 17x + 4x2 = 65 + -65

Combine like terms: 15 + -65 = -50
-50 + 17x + 4x2 = 65 + -65

Combine like terms: 65 + -65 = 0
-50 + 17x + 4x2 = 0

Factor a trinomial.
(-25 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-25 + -4x)' equal to zero and attempt to solve:

Simplifying
-25 + -4x = 0

Solving
-25 + -4x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -4x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -4x = 0 + 25
-4x = 0 + 25

Combine like terms: 0 + 25 = 25
-4x = 25

Divide each side by '-4'.
x = -6.25

Simplifying
x = -6.25

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6.25, 2}

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