(5x+6)(8x+11)=9x+11

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Solution for (5x+6)(8x+11)=9x+11 equation: 


Simplifying
(5x + 6)(8x + 11) = 9x + 11

Reorder the terms:
(6 + 5x)(8x + 11) = 9x + 11

Reorder the terms:
(6 + 5x)(11 + 8x) = 9x + 11

Multiply (6 + 5x) * (11 + 8x)
(6(11 + 8x) + 5x * (11 + 8x)) = 9x + 11
((11 * 6 + 8x * 6) + 5x * (11 + 8x)) = 9x + 11
((66 + 48x) + 5x * (11 + 8x)) = 9x + 11
(66 + 48x + (11 * 5x + 8x * 5x)) = 9x + 11
(66 + 48x + (55x + 40x2)) = 9x + 11

Combine like terms: 48x + 55x = 103x
(66 + 103x + 40x2) = 9x + 11

Reorder the terms:
66 + 103x + 40x2 = 11 + 9x

Solving
66 + 103x + 40x2 = 11 + 9x

Solving for variable 'x'.

Reorder the terms:
66 + -11 + 103x + -9x + 40x2 = 11 + 9x + -11 + -9x

Combine like terms: 66 + -11 = 55
55 + 103x + -9x + 40x2 = 11 + 9x + -11 + -9x

Combine like terms: 103x + -9x = 94x
55 + 94x + 40x2 = 11 + 9x + -11 + -9x

Reorder the terms:
55 + 94x + 40x2 = 11 + -11 + 9x + -9x

Combine like terms: 11 + -11 = 0
55 + 94x + 40x2 = 0 + 9x + -9x
55 + 94x + 40x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
55 + 94x + 40x2 = 0

Factor a trinomial.
(5 + 4x)(11 + 10x) = 0


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 '(11 + 10x)' equal to zero and attempt to solve:

Simplifying
11 + 10x = 0

Solving
11 + 10x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 10x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 10x = 0 + -11
10x = 0 + -11

Combine like terms: 0 + -11 = -11
10x = -11

Divide each side by '10'.
x = -1.1

Simplifying
x = -1.1
Solution
x = {-1.25, -1.1}

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