5(3x-2)(6x+5)=0

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Solution for 5(3x-2)(6x+5)=0 equation: 


Simplifying
5(3x + -2)(6x + 5) = 0

Reorder the terms:
5(-2 + 3x)(6x + 5) = 0

Reorder the terms:
5(-2 + 3x)(5 + 6x) = 0

Multiply (-2 + 3x) * (5 + 6x)
5(-2(5 + 6x) + 3x * (5 + 6x)) = 0
5((5 * -2 + 6x * -2) + 3x * (5 + 6x)) = 0
5((-10 + -12x) + 3x * (5 + 6x)) = 0
5(-10 + -12x + (5 * 3x + 6x * 3x)) = 0
5(-10 + -12x + (15x + 18x2)) = 0

Combine like terms: -12x + 15x = 3x
5(-10 + 3x + 18x2) = 0
(-10 * 5 + 3x * 5 + 18x2 * 5) = 0
(-50 + 15x + 90x2) = 0

Solving
-50 + 15x + 90x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + 3x + 18x2) = 0

Factor a trinomial.
5((-5 + -6x)(2 + -3x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 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 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-0.8333333333, 0.6666666667}

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