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

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


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

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

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

Multiply (7 + x) * (-1 + 2x)
(7(-1 + 2x) + x(-1 + 2x)) = (x + 7)(x + -2)
((-1 * 7 + 2x * 7) + x(-1 + 2x)) = (x + 7)(x + -2)
((-7 + 14x) + x(-1 + 2x)) = (x + 7)(x + -2)
(-7 + 14x + (-1 * x + 2x * x)) = (x + 7)(x + -2)
(-7 + 14x + (-1x + 2x2)) = (x + 7)(x + -2)

Combine like terms: 14x + -1x = 13x
(-7 + 13x + 2x2) = (x + 7)(x + -2)

Reorder the terms:
-7 + 13x + 2x2 = (7 + x)(x + -2)

Reorder the terms:
-7 + 13x + 2x2 = (7 + x)(-2 + x)

Multiply (7 + x) * (-2 + x)
-7 + 13x + 2x2 = (7(-2 + x) + x(-2 + x))
-7 + 13x + 2x2 = ((-2 * 7 + x * 7) + x(-2 + x))
-7 + 13x + 2x2 = ((-14 + 7x) + x(-2 + x))
-7 + 13x + 2x2 = (-14 + 7x + (-2 * x + x * x))
-7 + 13x + 2x2 = (-14 + 7x + (-2x + x2))

Combine like terms: 7x + -2x = 5x
-7 + 13x + 2x2 = (-14 + 5x + x2)

Solving
-7 + 13x + 2x2 = -14 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
-7 + 14 + 13x + -5x + 2x2 + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: -7 + 14 = 7
7 + 13x + -5x + 2x2 + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: 13x + -5x = 8x
7 + 8x + 2x2 + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
7 + 8x + 1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Reorder the terms:
7 + 8x + 1x2 = -14 + 14 + 5x + -5x + x2 + -1x2

Combine like terms: -14 + 14 = 0
7 + 8x + 1x2 = 0 + 5x + -5x + x2 + -1x2
7 + 8x + 1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
7 + 8x + 1x2 = 0 + x2 + -1x2
7 + 8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 8x + 1x2 = 0

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

Subproblem 1

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 2

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 = {-7, -1}

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