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

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


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

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

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

Multiply (-3 + 4x) * (5 + 4x)
7x(-3(5 + 4x) + 4x * (5 + 4x)) = 0
7x((5 * -3 + 4x * -3) + 4x * (5 + 4x)) = 0
7x((-15 + -12x) + 4x * (5 + 4x)) = 0
7x(-15 + -12x + (5 * 4x + 4x * 4x)) = 0
7x(-15 + -12x + (20x + 16x2)) = 0

Combine like terms: -12x + 20x = 8x
7x(-15 + 8x + 16x2) = 0
(-15 * 7x + 8x * 7x + 16x2 * 7x) = 0
(-105x + 56x2 + 112x3) = 0

Solving
-105x + 56x2 + 112x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x'.
7x(-15 + 8x + 16x2) = 0

Factor a trinomial.
7x((-5 + -4x)(3 + -4x)) = 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 '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

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

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

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 3
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0, -1.25, 0.75}

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