(x+9)(x-4)=(2x+2)(x-4)

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Solution for (x+9)(x-4)=(2x+2)(x-4) equation:


Simplifying
(x + 9)(x + -4) = (2x + 2)(x + -4)

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

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

Multiply (9 + x) * (-4 + x)
(9(-4 + x) + x(-4 + x)) = (2x + 2)(x + -4)
((-4 * 9 + x * 9) + x(-4 + x)) = (2x + 2)(x + -4)
((-36 + 9x) + x(-4 + x)) = (2x + 2)(x + -4)
(-36 + 9x + (-4 * x + x * x)) = (2x + 2)(x + -4)
(-36 + 9x + (-4x + x2)) = (2x + 2)(x + -4)

Combine like terms: 9x + -4x = 5x
(-36 + 5x + x2) = (2x + 2)(x + -4)

Reorder the terms:
-36 + 5x + x2 = (2 + 2x)(x + -4)

Reorder the terms:
-36 + 5x + x2 = (2 + 2x)(-4 + x)

Multiply (2 + 2x) * (-4 + x)
-36 + 5x + x2 = (2(-4 + x) + 2x * (-4 + x))
-36 + 5x + x2 = ((-4 * 2 + x * 2) + 2x * (-4 + x))
-36 + 5x + x2 = ((-8 + 2x) + 2x * (-4 + x))
-36 + 5x + x2 = (-8 + 2x + (-4 * 2x + x * 2x))
-36 + 5x + x2 = (-8 + 2x + (-8x + 2x2))

Combine like terms: 2x + -8x = -6x
-36 + 5x + x2 = (-8 + -6x + 2x2)

Solving
-36 + 5x + x2 = -8 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-36 + 8 + 5x + 6x + x2 + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Combine like terms: -36 + 8 = -28
-28 + 5x + 6x + x2 + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Combine like terms: 5x + 6x = 11x
-28 + 11x + x2 + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-28 + 11x + -1x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Reorder the terms:
-28 + 11x + -1x2 = -8 + 8 + -6x + 6x + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
-28 + 11x + -1x2 = 0 + -6x + 6x + 2x2 + -2x2
-28 + 11x + -1x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
-28 + 11x + -1x2 = 0 + 2x2 + -2x2
-28 + 11x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-28 + 11x + -1x2 = 0

Factor a trinomial.
(-7 + x)(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {7, 4}

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