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

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


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

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

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

Multiply (4 + x) * (-3 + 2x)
(4(-3 + 2x) + x(-3 + 2x)) = (x + 4)(x + 2)
((-3 * 4 + 2x * 4) + x(-3 + 2x)) = (x + 4)(x + 2)
((-12 + 8x) + x(-3 + 2x)) = (x + 4)(x + 2)
(-12 + 8x + (-3 * x + 2x * x)) = (x + 4)(x + 2)
(-12 + 8x + (-3x + 2x2)) = (x + 4)(x + 2)

Combine like terms: 8x + -3x = 5x
(-12 + 5x + 2x2) = (x + 4)(x + 2)

Reorder the terms:
-12 + 5x + 2x2 = (4 + x)(x + 2)

Reorder the terms:
-12 + 5x + 2x2 = (4 + x)(2 + x)

Multiply (4 + x) * (2 + x)
-12 + 5x + 2x2 = (4(2 + x) + x(2 + x))
-12 + 5x + 2x2 = ((2 * 4 + x * 4) + x(2 + x))
-12 + 5x + 2x2 = ((8 + 4x) + x(2 + x))
-12 + 5x + 2x2 = (8 + 4x + (2 * x + x * x))
-12 + 5x + 2x2 = (8 + 4x + (2x + x2))

Combine like terms: 4x + 2x = 6x
-12 + 5x + 2x2 = (8 + 6x + x2)

Solving
-12 + 5x + 2x2 = 8 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + -8 + 5x + -6x + 2x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: -12 + -8 = -20
-20 + 5x + -6x + 2x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: 5x + -6x = -1x
-20 + -1x + 2x2 + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-20 + -1x + 1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Reorder the terms:
-20 + -1x + 1x2 = 8 + -8 + 6x + -6x + x2 + -1x2

Combine like terms: 8 + -8 = 0
-20 + -1x + 1x2 = 0 + 6x + -6x + x2 + -1x2
-20 + -1x + 1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-20 + -1x + 1x2 = 0 + x2 + -1x2
-20 + -1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -1x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-4, 5}

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