(x-7)(8x+2)=-22(x-7)

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Solution for (x-7)(8x+2)=-22(x-7) equation: 


Simplifying
(x + -7)(8x + 2) = -22(x + -7)

Reorder the terms:
(-7 + x)(8x + 2) = -22(x + -7)

Reorder the terms:
(-7 + x)(2 + 8x) = -22(x + -7)

Multiply (-7 + x) * (2 + 8x)
(-7(2 + 8x) + x(2 + 8x)) = -22(x + -7)
((2 * -7 + 8x * -7) + x(2 + 8x)) = -22(x + -7)
((-14 + -56x) + x(2 + 8x)) = -22(x + -7)
(-14 + -56x + (2 * x + 8x * x)) = -22(x + -7)
(-14 + -56x + (2x + 8x2)) = -22(x + -7)

Combine like terms: -56x + 2x = -54x
(-14 + -54x + 8x2) = -22(x + -7)

Reorder the terms:
-14 + -54x + 8x2 = -22(-7 + x)
-14 + -54x + 8x2 = (-7 * -22 + x * -22)
-14 + -54x + 8x2 = (154 + -22x)

Solving
-14 + -54x + 8x2 = 154 + -22x

Solving for variable 'x'.

Reorder the terms:
-14 + -154 + -54x + 22x + 8x2 = 154 + -22x + -154 + 22x

Combine like terms: -14 + -154 = -168
-168 + -54x + 22x + 8x2 = 154 + -22x + -154 + 22x

Combine like terms: -54x + 22x = -32x
-168 + -32x + 8x2 = 154 + -22x + -154 + 22x

Reorder the terms:
-168 + -32x + 8x2 = 154 + -154 + -22x + 22x

Combine like terms: 154 + -154 = 0
-168 + -32x + 8x2 = 0 + -22x + 22x
-168 + -32x + 8x2 = -22x + 22x

Combine like terms: -22x + 22x = 0
-168 + -32x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-21 + -4x + x2) = 0

Factor a trinomial.
8((-3 + -1x)(7 + -1x)) = 0

Ignore the factor 8.

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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-3, 7}

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