4x(3x+6)(5x-7)=0

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Solution for 4x(3x+6)(5x-7)=0 equation: 


Simplifying
4x(3x + 6)(5x + -7) = 0

Reorder the terms:
4x(6 + 3x)(5x + -7) = 0

Reorder the terms:
4x(6 + 3x)(-7 + 5x) = 0

Multiply (6 + 3x) * (-7 + 5x)
4x(6(-7 + 5x) + 3x * (-7 + 5x)) = 0
4x((-7 * 6 + 5x * 6) + 3x * (-7 + 5x)) = 0
4x((-42 + 30x) + 3x * (-7 + 5x)) = 0
4x(-42 + 30x + (-7 * 3x + 5x * 3x)) = 0
4x(-42 + 30x + (-21x + 15x2)) = 0

Combine like terms: 30x + -21x = 9x
4x(-42 + 9x + 15x2) = 0
(-42 * 4x + 9x * 4x + 15x2 * 4x) = 0
(-168x + 36x2 + 60x3) = 0

Solving
-168x + 36x2 + 60x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(-14 + 3x + 5x2) = 0

Factor a trinomial.
12x((-2 + -1x)(7 + -5x)) = 0

Ignore the factor 12.

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 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 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 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {0, -2, 1.4}

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