x^2-14x+40=2x^2-16x+32

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Solution for x^2-14x+40=2x^2-16x+32 equation:


Simplifying
x2 + -14x + 40 = 2x2 + -16x + 32

Reorder the terms:
40 + -14x + x2 = 2x2 + -16x + 32

Reorder the terms:
40 + -14x + x2 = 32 + -16x + 2x2

Solving
40 + -14x + x2 = 32 + -16x + 2x2

Solving for variable 'x'.

Reorder the terms:
40 + -32 + -14x + 16x + x2 + -2x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Combine like terms: 40 + -32 = 8
8 + -14x + 16x + x2 + -2x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Combine like terms: -14x + 16x = 2x
8 + 2x + x2 + -2x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Combine like terms: x2 + -2x2 = -1x2
8 + 2x + -1x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Reorder the terms:
8 + 2x + -1x2 = 32 + -32 + -16x + 16x + 2x2 + -2x2

Combine like terms: 32 + -32 = 0
8 + 2x + -1x2 = 0 + -16x + 16x + 2x2 + -2x2
8 + 2x + -1x2 = -16x + 16x + 2x2 + -2x2

Combine like terms: -16x + 16x = 0
8 + 2x + -1x2 = 0 + 2x2 + -2x2
8 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + 2x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(2 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {4, -2}

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