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

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


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

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

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

Multiply (4 + x) * (-2 + x)
(4(-2 + x) + x(-2 + x)) = 7x + -2
((-2 * 4 + x * 4) + x(-2 + x)) = 7x + -2
((-8 + 4x) + x(-2 + x)) = 7x + -2
(-8 + 4x + (-2 * x + x * x)) = 7x + -2
(-8 + 4x + (-2x + x2)) = 7x + -2

Combine like terms: 4x + -2x = 2x
(-8 + 2x + x2) = 7x + -2

Reorder the terms:
-8 + 2x + x2 = -2 + 7x

Solving
-8 + 2x + x2 = -2 + 7x

Solving for variable 'x'.

Reorder the terms:
-8 + 2 + 2x + -7x + x2 = -2 + 7x + 2 + -7x

Combine like terms: -8 + 2 = -6
-6 + 2x + -7x + x2 = -2 + 7x + 2 + -7x

Combine like terms: 2x + -7x = -5x
-6 + -5x + x2 = -2 + 7x + 2 + -7x

Reorder the terms:
-6 + -5x + x2 = -2 + 2 + 7x + -7x

Combine like terms: -2 + 2 = 0
-6 + -5x + x2 = 0 + 7x + -7x
-6 + -5x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-6 + -5x + x2 = 0

Factor a trinomial.
(-1 + -1x)(6 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}

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