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

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


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

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

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

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

Combine like terms: -18x + 10x = -8x
5(-15 + -8x + 12x2) = 0
(-15 * 5 + -8x * 5 + 12x2 * 5) = 0
(-75 + -40x + 60x2) = 0

Solving
-75 + -40x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + -8x + 12x2) = 0

Factor a trinomial.
5((-5 + -6x)(3 + -2x)) = 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.8333333333, 1.5}

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