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

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


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

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

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

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

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

Reorder the terms:
-28 + 3x + x2 = 2(-4 + x)
-28 + 3x + x2 = (-4 * 2 + x * 2)
-28 + 3x + x2 = (-8 + 2x)

Solving
-28 + 3x + x2 = -8 + 2x

Solving for variable 'x'.

Reorder the terms:
-28 + 8 + 3x + -2x + x2 = -8 + 2x + 8 + -2x

Combine like terms: -28 + 8 = -20
-20 + 3x + -2x + x2 = -8 + 2x + 8 + -2x

Combine like terms: 3x + -2x = 1x
-20 + 1x + x2 = -8 + 2x + 8 + -2x

Reorder the terms:
-20 + 1x + x2 = -8 + 8 + 2x + -2x

Combine like terms: -8 + 8 = 0
-20 + 1x + x2 = 0 + 2x + -2x
-20 + 1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-20 + 1x + x2 = 0

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


Subproblem 1
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

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 = {-5, 4}

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