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

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


Simplifying
(2x + -1)(4) = (x + -2)(x + 7)

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

Reorder the terms for easier multiplication:
4(-1 + 2x) = (x + -2)(x + 7)
(-1 * 4 + 2x * 4) = (x + -2)(x + 7)
(-4 + 8x) = (x + -2)(x + 7)

Reorder the terms:
-4 + 8x = (-2 + x)(x + 7)

Reorder the terms:
-4 + 8x = (-2 + x)(7 + x)

Multiply (-2 + x) * (7 + x)
-4 + 8x = (-2(7 + x) + x(7 + x))
-4 + 8x = ((7 * -2 + x * -2) + x(7 + x))
-4 + 8x = ((-14 + -2x) + x(7 + x))
-4 + 8x = (-14 + -2x + (7 * x + x * x))
-4 + 8x = (-14 + -2x + (7x + x2))

Combine like terms: -2x + 7x = 5x
-4 + 8x = (-14 + 5x + x2)

Solving
-4 + 8x = -14 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 14 + 8x + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: -4 + 14 = 10
10 + 8x + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: 8x + -5x = 3x
10 + 3x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Reorder the terms:
10 + 3x + -1x2 = -14 + 14 + 5x + -5x + x2 + -1x2

Combine like terms: -14 + 14 = 0
10 + 3x + -1x2 = 0 + 5x + -5x + x2 + -1x2
10 + 3x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
10 + 3x + -1x2 = 0 + x2 + -1x2
10 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 3x + -1x2 = 0

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


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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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 = {5, -2}

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