-7x(x-2)+1=15-7x

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Solution for -7x(x-2)+1=15-7x equation: 


Simplifying
-7x(x + -2) + 1 = 15 + -7x

Reorder the terms:
-7x(-2 + x) + 1 = 15 + -7x
(-2 * -7x + x * -7x) + 1 = 15 + -7x
(14x + -7x2) + 1 = 15 + -7x

Reorder the terms:
1 + 14x + -7x2 = 15 + -7x

Solving
1 + 14x + -7x2 = 15 + -7x

Solving for variable 'x'.

Reorder the terms:
1 + -15 + 14x + 7x + -7x2 = 15 + -7x + -15 + 7x

Combine like terms: 1 + -15 = -14
-14 + 14x + 7x + -7x2 = 15 + -7x + -15 + 7x

Combine like terms: 14x + 7x = 21x
-14 + 21x + -7x2 = 15 + -7x + -15 + 7x

Reorder the terms:
-14 + 21x + -7x2 = 15 + -15 + -7x + 7x

Combine like terms: 15 + -15 = 0
-14 + 21x + -7x2 = 0 + -7x + 7x
-14 + 21x + -7x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-14 + 21x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-2 + 3x + -1x2) = 0

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

Ignore the factor 7.

Subproblem 1
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

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
Solution
x = {2, 1}

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