7x(2x-4)(5x+3)=0

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Solution for 7x(2x-4)(5x+3)=0 equation: 


Simplifying
7x(2x + -4)(5x + 3) = 0

Reorder the terms:
7x(-4 + 2x)(5x + 3) = 0

Reorder the terms:
7x(-4 + 2x)(3 + 5x) = 0

Multiply (-4 + 2x) * (3 + 5x)
7x(-4(3 + 5x) + 2x * (3 + 5x)) = 0
7x((3 * -4 + 5x * -4) + 2x * (3 + 5x)) = 0
7x((-12 + -20x) + 2x * (3 + 5x)) = 0
7x(-12 + -20x + (3 * 2x + 5x * 2x)) = 0
7x(-12 + -20x + (6x + 10x2)) = 0

Combine like terms: -20x + 6x = -14x
7x(-12 + -14x + 10x2) = 0
(-12 * 7x + -14x * 7x + 10x2 * 7x) = 0
(-84x + -98x2 + 70x3) = 0

Solving
-84x + -98x2 + 70x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14x'.
14x(-6 + -7x + 5x2) = 0

Factor a trinomial.
14x((-3 + -5x)(2 + -1x)) = 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 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 3
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
Solution
x = {0, -0.6, 2}

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