2(x-1)x-7=18-5(x+4)

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Solution for 2(x-1)x-7=18-5(x+4) equation: 


Simplifying
2(x + -1) * x + -7 = 18 + -5(x + 4)

Reorder the terms:
2(-1 + x) * x + -7 = 18 + -5(x + 4)

Reorder the terms for easier multiplication:
2x(-1 + x) + -7 = 18 + -5(x + 4)
(-1 * 2x + x * 2x) + -7 = 18 + -5(x + 4)
(-2x + 2x2) + -7 = 18 + -5(x + 4)

Reorder the terms:
-7 + -2x + 2x2 = 18 + -5(x + 4)

Reorder the terms:
-7 + -2x + 2x2 = 18 + -5(4 + x)
-7 + -2x + 2x2 = 18 + (4 * -5 + x * -5)
-7 + -2x + 2x2 = 18 + (-20 + -5x)

Combine like terms: 18 + -20 = -2
-7 + -2x + 2x2 = -2 + -5x

Solving
-7 + -2x + 2x2 = -2 + -5x

Solving for variable 'x'.

Reorder the terms:
-7 + 2 + -2x + 5x + 2x2 = -2 + -5x + 2 + 5x

Combine like terms: -7 + 2 = -5
-5 + -2x + 5x + 2x2 = -2 + -5x + 2 + 5x

Combine like terms: -2x + 5x = 3x
-5 + 3x + 2x2 = -2 + -5x + 2 + 5x

Reorder the terms:
-5 + 3x + 2x2 = -2 + 2 + -5x + 5x

Combine like terms: -2 + 2 = 0
-5 + 3x + 2x2 = 0 + -5x + 5x
-5 + 3x + 2x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-5 + 3x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 1}

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