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

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


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

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

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

Multiply (4 + x) * (-7 + x)
(4(-7 + x) + x(-7 + x)) = (2x + 7)(x + -7)
((-7 * 4 + x * 4) + x(-7 + x)) = (2x + 7)(x + -7)
((-28 + 4x) + x(-7 + x)) = (2x + 7)(x + -7)
(-28 + 4x + (-7 * x + x * x)) = (2x + 7)(x + -7)
(-28 + 4x + (-7x + x2)) = (2x + 7)(x + -7)

Combine like terms: 4x + -7x = -3x
(-28 + -3x + x2) = (2x + 7)(x + -7)

Reorder the terms:
-28 + -3x + x2 = (7 + 2x)(x + -7)

Reorder the terms:
-28 + -3x + x2 = (7 + 2x)(-7 + x)

Multiply (7 + 2x) * (-7 + x)
-28 + -3x + x2 = (7(-7 + x) + 2x * (-7 + x))
-28 + -3x + x2 = ((-7 * 7 + x * 7) + 2x * (-7 + x))
-28 + -3x + x2 = ((-49 + 7x) + 2x * (-7 + x))
-28 + -3x + x2 = (-49 + 7x + (-7 * 2x + x * 2x))
-28 + -3x + x2 = (-49 + 7x + (-14x + 2x2))

Combine like terms: 7x + -14x = -7x
-28 + -3x + x2 = (-49 + -7x + 2x2)

Solving
-28 + -3x + x2 = -49 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-28 + 49 + -3x + 7x + x2 + -2x2 = -49 + -7x + 2x2 + 49 + 7x + -2x2

Combine like terms: -28 + 49 = 21
21 + -3x + 7x + x2 + -2x2 = -49 + -7x + 2x2 + 49 + 7x + -2x2

Combine like terms: -3x + 7x = 4x
21 + 4x + x2 + -2x2 = -49 + -7x + 2x2 + 49 + 7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
21 + 4x + -1x2 = -49 + -7x + 2x2 + 49 + 7x + -2x2

Reorder the terms:
21 + 4x + -1x2 = -49 + 49 + -7x + 7x + 2x2 + -2x2

Combine like terms: -49 + 49 = 0
21 + 4x + -1x2 = 0 + -7x + 7x + 2x2 + -2x2
21 + 4x + -1x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
21 + 4x + -1x2 = 0 + 2x2 + -2x2
21 + 4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
21 + 4x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(3 + x) = 0

Subproblem 1

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {7, -3}

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