=-2x(7-x(3x-5)+x^2)

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Solution for =-2x(7-x(3x-5)+x^2) equation: 


Simplifying
0 = -2x(7 + -1x(3x + -5) + x2)

Reorder the terms:
0 = -2x(7 + -1x(-5 + 3x) + x2)
0 = -2x(7 + (-5 * -1x + 3x * -1x) + x2)
0 = -2x(7 + (5x + -3x2) + x2)

Combine like terms: -3x2 + x2 = -2x2
0 = -2x(7 + 5x + -2x2)
0 = (7 * -2x + 5x * -2x + -2x2 * -2x)
0 = (-14x + -10x2 + 4x3)

Solving
0 = -14x + -10x2 + 4x3

Solving for variable 'x'.
Remove the zero:
14x + 10x2 + -4x3 = -14x + -10x2 + 4x3 + 14x + 10x2 + -4x3

Reorder the terms:
14x + 10x2 + -4x3 = -14x + 14x + -10x2 + 10x2 + 4x3 + -4x3

Combine like terms: -14x + 14x = 0
14x + 10x2 + -4x3 = 0 + -10x2 + 10x2 + 4x3 + -4x3
14x + 10x2 + -4x3 = -10x2 + 10x2 + 4x3 + -4x3

Combine like terms: -10x2 + 10x2 = 0
14x + 10x2 + -4x3 = 0 + 4x3 + -4x3
14x + 10x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
14x + 10x2 + -4x3 = 0

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

Factor a trinomial.
2x((7 + -2x)(1 + x)) = 0

Ignore the factor 2.

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0, 3.5, -1}

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