(3x+11)90(4x-5)=

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Solution for (3x+11)90(4x-5)= equation: 


Simplifying
(3x + 11) * 90(4x + -5) = 0

Reorder the terms:
(11 + 3x) * 90(4x + -5) = 0

Reorder the terms:
(11 + 3x) * 90(-5 + 4x) = 0

Reorder the terms for easier multiplication:
90(11 + 3x)(-5 + 4x) = 0

Multiply (11 + 3x) * (-5 + 4x)
90(11(-5 + 4x) + 3x * (-5 + 4x)) = 0
90((-5 * 11 + 4x * 11) + 3x * (-5 + 4x)) = 0
90((-55 + 44x) + 3x * (-5 + 4x)) = 0
90(-55 + 44x + (-5 * 3x + 4x * 3x)) = 0
90(-55 + 44x + (-15x + 12x2)) = 0

Combine like terms: 44x + -15x = 29x
90(-55 + 29x + 12x2) = 0
(-55 * 90 + 29x * 90 + 12x2 * 90) = 0
(-4950 + 2610x + 1080x2) = 0

Solving
-4950 + 2610x + 1080x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '90'.
90(-55 + 29x + 12x2) = 0

Factor a trinomial.
90((-11 + -3x)(5 + -4x)) = 0

Ignore the factor 90.

Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 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 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667

Subproblem 2
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
Solution
x = {-3.666666667, 1.25}

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