5x(5x-7)(8x+5)=0

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Solution for 5x(5x-7)(8x+5)=0 equation: 


Simplifying
5x(5x + -7)(8x + 5) = 0

Reorder the terms:
5x(-7 + 5x)(8x + 5) = 0

Reorder the terms:
5x(-7 + 5x)(5 + 8x) = 0

Multiply (-7 + 5x) * (5 + 8x)
5x(-7(5 + 8x) + 5x * (5 + 8x)) = 0
5x((5 * -7 + 8x * -7) + 5x * (5 + 8x)) = 0
5x((-35 + -56x) + 5x * (5 + 8x)) = 0
5x(-35 + -56x + (5 * 5x + 8x * 5x)) = 0
5x(-35 + -56x + (25x + 40x2)) = 0

Combine like terms: -56x + 25x = -31x
5x(-35 + -31x + 40x2) = 0
(-35 * 5x + -31x * 5x + 40x2 * 5x) = 0
(-175x + -155x2 + 200x3) = 0

Solving
-175x + -155x2 + 200x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-35 + -31x + 40x2) = 0

Factor a trinomial.
5x((-5 + -8x)(7 + -5x)) = 0

Ignore the factor 5.

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 + -8x)' equal to zero and attempt to solve:

Simplifying
-5 + -8x = 0

Solving
-5 + -8x = 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 + -8x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8x = 0 + 5
-8x = 0 + 5

Combine like terms: 0 + 5 = 5
-8x = 5

Divide each side by '-8'.
x = -0.625

Simplifying
x = -0.625

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, -0.625, 1.4}

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