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

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


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

Reorder the terms:
3x(5 + 4x) + -5(4x + 5) = 0
(5 * 3x + 4x * 3x) + -5(4x + 5) = 0
(15x + 12x2) + -5(4x + 5) = 0

Reorder the terms:
15x + 12x2 + -5(5 + 4x) = 0
15x + 12x2 + (5 * -5 + 4x * -5) = 0
15x + 12x2 + (-25 + -20x) = 0

Reorder the terms:
-25 + 15x + -20x + 12x2 = 0

Combine like terms: 15x + -20x = -5x
-25 + -5x + 12x2 = 0

Solving
-25 + -5x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -4x)(5 + -3x) = 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 '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-1.25, 1.666666667}

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