(x+3)(x-4)=(2x+2)(x-4)

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Solution for (x+3)(x-4)=(2x+2)(x-4) equation: 


Simplifying
(x + 3)(x + -4) = (2x + 2)(x + -4)

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

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

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) = (2x + 2)(x + -4)
((-4 * 3 + x * 3) + x(-4 + x)) = (2x + 2)(x + -4)
((-12 + 3x) + x(-4 + x)) = (2x + 2)(x + -4)
(-12 + 3x + (-4 * x + x * x)) = (2x + 2)(x + -4)
(-12 + 3x + (-4x + x2)) = (2x + 2)(x + -4)

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) = (2x + 2)(x + -4)

Reorder the terms:
-12 + -1x + x2 = (2 + 2x)(x + -4)

Reorder the terms:
-12 + -1x + x2 = (2 + 2x)(-4 + x)

Multiply (2 + 2x) * (-4 + x)
-12 + -1x + x2 = (2(-4 + x) + 2x * (-4 + x))
-12 + -1x + x2 = ((-4 * 2 + x * 2) + 2x * (-4 + x))
-12 + -1x + x2 = ((-8 + 2x) + 2x * (-4 + x))
-12 + -1x + x2 = (-8 + 2x + (-4 * 2x + x * 2x))
-12 + -1x + x2 = (-8 + 2x + (-8x + 2x2))

Combine like terms: 2x + -8x = -6x
-12 + -1x + x2 = (-8 + -6x + 2x2)

Solving
-12 + -1x + x2 = -8 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-12 + 8 + -1x + 6x + x2 + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Combine like terms: -12 + 8 = -4
-4 + -1x + 6x + x2 + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Combine like terms: -1x + 6x = 5x
-4 + 5x + x2 + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-4 + 5x + -1x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Reorder the terms:
-4 + 5x + -1x2 = -8 + 8 + -6x + 6x + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
-4 + 5x + -1x2 = 0 + -6x + 6x + 2x2 + -2x2
-4 + 5x + -1x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
-4 + 5x + -1x2 = 0 + 2x2 + -2x2
-4 + 5x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 5x + -1x2 = 0

Factor a trinomial.
(-4 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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 = {4, 1}

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