5x(2x-7)(x+1)=0

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Solution for 5x(2x-7)(x+1)=0 equation: 


Simplifying
5x(2x + -7)(x + 1) = 0

Reorder the terms:
5x(-7 + 2x)(x + 1) = 0

Reorder the terms:
5x(-7 + 2x)(1 + x) = 0

Multiply (-7 + 2x) * (1 + x)
5x(-7(1 + x) + 2x * (1 + x)) = 0
5x((1 * -7 + x * -7) + 2x * (1 + x)) = 0
5x((-7 + -7x) + 2x * (1 + x)) = 0
5x(-7 + -7x + (1 * 2x + x * 2x)) = 0
5x(-7 + -7x + (2x + 2x2)) = 0

Combine like terms: -7x + 2x = -5x
5x(-7 + -5x + 2x2) = 0
(-7 * 5x + -5x * 5x + 2x2 * 5x) = 0
(-35x + -25x2 + 10x3) = 0

Solving
-35x + -25x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-7 + -5x + 2x2) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 3
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
Solution
x = {0, -1, 3.5}

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