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

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


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

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

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

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

Combine like terms: -12x + 5x = -7x
3(-15 + -7x + 4x2) = 0
(-15 * 3 + -7x * 3 + 4x2 * 3) = 0
(-45 + -21x + 12x2) = 0

Solving
-45 + -21x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -7x + 4x2) = 0

Factor a trinomial.
3((-5 + -4x)(3 + -1x)) = 0

Ignore the factor 3.

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.25, 3}

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