5x(x-10)(4x+7)=0

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Solution for 5x(x-10)(4x+7)=0 equation: 


Simplifying
5x(x + -10)(4x + 7) = 0

Reorder the terms:
5x(-10 + x)(4x + 7) = 0

Reorder the terms:
5x(-10 + x)(7 + 4x) = 0

Multiply (-10 + x) * (7 + 4x)
5x(-10(7 + 4x) + x(7 + 4x)) = 0
5x((7 * -10 + 4x * -10) + x(7 + 4x)) = 0
5x((-70 + -40x) + x(7 + 4x)) = 0
5x(-70 + -40x + (7 * x + 4x * x)) = 0
5x(-70 + -40x + (7x + 4x2)) = 0

Combine like terms: -40x + 7x = -33x
5x(-70 + -33x + 4x2) = 0
(-70 * 5x + -33x * 5x + 4x2 * 5x) = 0
(-350x + -165x2 + 20x3) = 0

Solving
-350x + -165x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-70 + -33x + 4x2) = 0

Factor a trinomial.
5x((-7 + -4x)(10 + -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 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 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 + -4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x = 0 + 7
-4x = 0 + 7

Combine like terms: 0 + 7 = 7
-4x = 7

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75

Subproblem 3
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0, -1.75, 10}

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