(x-4)(x+7)=x(2)-22

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Solution for (x-4)(x+7)=x(2)-22 equation: 


Simplifying
(x + -4)(x + 7) = x(2) + -22

Reorder the terms:
(-4 + x)(x + 7) = x(2) + -22

Reorder the terms:
(-4 + x)(7 + x) = x(2) + -22

Multiply (-4 + x) * (7 + x)
(-4(7 + x) + x(7 + x)) = x(2) + -22
((7 * -4 + x * -4) + x(7 + x)) = x(2) + -22
((-28 + -4x) + x(7 + x)) = x(2) + -22
(-28 + -4x + (7 * x + x * x)) = x(2) + -22
(-28 + -4x + (7x + x2)) = x(2) + -22

Combine like terms: -4x + 7x = 3x
(-28 + 3x + x2) = x(2) + -22

Reorder the terms for easier multiplication:
-28 + 3x + x2 = 2x + -22

Reorder the terms:
-28 + 3x + x2 = -22 + 2x

Solving
-28 + 3x + x2 = -22 + 2x

Solving for variable 'x'.

Reorder the terms:
-28 + 22 + 3x + -2x + x2 = -22 + 2x + 22 + -2x

Combine like terms: -28 + 22 = -6
-6 + 3x + -2x + x2 = -22 + 2x + 22 + -2x

Combine like terms: 3x + -2x = 1x
-6 + 1x + x2 = -22 + 2x + 22 + -2x

Reorder the terms:
-6 + 1x + x2 = -22 + 22 + 2x + -2x

Combine like terms: -22 + 22 = 0
-6 + 1x + x2 = 0 + 2x + -2x
-6 + 1x + x2 = 2x + -2x

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

Factor a trinomial.
(-3 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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