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

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


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

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

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

Multiply (3 + x) * (-6 + 4x)
7x(3(-6 + 4x) + x(-6 + 4x)) = 0
7x((-6 * 3 + 4x * 3) + x(-6 + 4x)) = 0
7x((-18 + 12x) + x(-6 + 4x)) = 0
7x(-18 + 12x + (-6 * x + 4x * x)) = 0
7x(-18 + 12x + (-6x + 4x2)) = 0

Combine like terms: 12x + -6x = 6x
7x(-18 + 6x + 4x2) = 0
(-18 * 7x + 6x * 7x + 4x2 * 7x) = 0
(-126x + 42x2 + 28x3) = 0

Solving
-126x + 42x2 + 28x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14x'.
14x(-9 + 3x + 2x2) = 0

Factor a trinomial.
14x((-3 + -1x)(3 + -2x)) = 0

Ignore the factor 14.

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 '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 3
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, -3, 1.5}

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