10(3x-4)(x+6)=0

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Solution for 10(3x-4)(x+6)=0 equation: 


Simplifying
10(3x + -4)(x + 6) = 0

Reorder the terms:
10(-4 + 3x)(x + 6) = 0

Reorder the terms:
10(-4 + 3x)(6 + x) = 0

Multiply (-4 + 3x) * (6 + x)
10(-4(6 + x) + 3x * (6 + x)) = 0
10((6 * -4 + x * -4) + 3x * (6 + x)) = 0
10((-24 + -4x) + 3x * (6 + x)) = 0
10(-24 + -4x + (6 * 3x + x * 3x)) = 0
10(-24 + -4x + (18x + 3x2)) = 0

Combine like terms: -4x + 18x = 14x
10(-24 + 14x + 3x2) = 0
(-24 * 10 + 14x * 10 + 3x2 * 10) = 0
(-240 + 140x + 30x2) = 0

Solving
-240 + 140x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-24 + 14x + 3x2) = 0

Factor a trinomial.
10((-6 + -1x)(4 + -3x)) = 0

Ignore the factor 10.

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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-6, 1.333333333}

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