(3x-1)(4x+5)+5=0

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Solution for (3x-1)(4x+5)+5=0 equation: 


Simplifying
(3x + -1)(4x + 5) + 5 = 0

Reorder the terms:
(-1 + 3x)(4x + 5) + 5 = 0

Reorder the terms:
(-1 + 3x)(5 + 4x) + 5 = 0

Multiply (-1 + 3x) * (5 + 4x)
(-1(5 + 4x) + 3x * (5 + 4x)) + 5 = 0
((5 * -1 + 4x * -1) + 3x * (5 + 4x)) + 5 = 0
((-5 + -4x) + 3x * (5 + 4x)) + 5 = 0
(-5 + -4x + (5 * 3x + 4x * 3x)) + 5 = 0
(-5 + -4x + (15x + 12x2)) + 5 = 0

Combine like terms: -4x + 15x = 11x
(-5 + 11x + 12x2) + 5 = 0

Reorder the terms:
-5 + 5 + 11x + 12x2 = 0

Combine like terms: -5 + 5 = 0
0 + 11x + 12x2 = 0
11x + 12x2 = 0

Solving
11x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(11 + 12x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(11 + 12x)' equal to zero and attempt to solve:

Simplifying
11 + 12x = 0

Solving
11 + 12x = 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 + 12x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 12x = 0 + -11
12x = 0 + -11

Combine like terms: 0 + -11 = -11
12x = -11

Divide each side by '12'.
x = -0.9166666667

Simplifying
x = -0.9166666667
Solution
x = {0, -0.9166666667}

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