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

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


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

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

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

Multiply (-4 + x) * (-7 + 2x)
5x(-4(-7 + 2x) + x(-7 + 2x)) = 0
5x((-7 * -4 + 2x * -4) + x(-7 + 2x)) = 0
5x((28 + -8x) + x(-7 + 2x)) = 0
5x(28 + -8x + (-7 * x + 2x * x)) = 0
5x(28 + -8x + (-7x + 2x2)) = 0

Combine like terms: -8x + -7x = -15x
5x(28 + -15x + 2x2) = 0
(28 * 5x + -15x * 5x + 2x2 * 5x) = 0
(140x + -75x2 + 10x3) = 0

Solving
140x + -75x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(28 + -15x + 2x2) = 0

Factor a trinomial.
5x((7 + -2x)(4 + -1x)) = 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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 3.5, 4}

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