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

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


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

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

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

Multiply (3 + x) * (-4 + 5x)
7x(3(-4 + 5x) + x(-4 + 5x)) = 0
7x((-4 * 3 + 5x * 3) + x(-4 + 5x)) = 0
7x((-12 + 15x) + x(-4 + 5x)) = 0
7x(-12 + 15x + (-4 * x + 5x * x)) = 0
7x(-12 + 15x + (-4x + 5x2)) = 0

Combine like terms: 15x + -4x = 11x
7x(-12 + 11x + 5x2) = 0
(-12 * 7x + 11x * 7x + 5x2 * 7x) = 0
(-84x + 77x2 + 35x3) = 0

Solving
-84x + 77x2 + 35x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x'.
7x(-12 + 11x + 5x2) = 0

Factor a trinomial.
7x((-3 + -1x)(4 + -5x)) = 0

Ignore the factor 7.

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 '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {0, -3, 0.8}

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