5x(x+2)(6x-7)=0

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Solution for 5x(x+2)(6x-7)=0 equation: 


Simplifying
5x(x + 2)(6x + -7) = 0

Reorder the terms:
5x(2 + x)(6x + -7) = 0

Reorder the terms:
5x(2 + x)(-7 + 6x) = 0

Multiply (2 + x) * (-7 + 6x)
5x(2(-7 + 6x) + x(-7 + 6x)) = 0
5x((-7 * 2 + 6x * 2) + x(-7 + 6x)) = 0
5x((-14 + 12x) + x(-7 + 6x)) = 0
5x(-14 + 12x + (-7 * x + 6x * x)) = 0
5x(-14 + 12x + (-7x + 6x2)) = 0

Combine like terms: 12x + -7x = 5x
5x(-14 + 5x + 6x2) = 0
(-14 * 5x + 5x * 5x + 6x2 * 5x) = 0
(-70x + 25x2 + 30x3) = 0

Solving
-70x + 25x2 + 30x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-14 + 5x + 6x2) = 0

Factor a trinomial.
5x((-2 + -1x)(7 + -6x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {0, -2, 1.166666667}

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