(x-9)(8x+2)=-22(x-9)

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Solution for (x-9)(8x+2)=-22(x-9) equation:


Simplifying
(x + -9)(8x + 2) = -22(x + -9)

Reorder the terms:
(-9 + x)(8x + 2) = -22(x + -9)

Reorder the terms:
(-9 + x)(2 + 8x) = -22(x + -9)

Multiply (-9 + x) * (2 + 8x)
(-9(2 + 8x) + x(2 + 8x)) = -22(x + -9)
((2 * -9 + 8x * -9) + x(2 + 8x)) = -22(x + -9)
((-18 + -72x) + x(2 + 8x)) = -22(x + -9)
(-18 + -72x + (2 * x + 8x * x)) = -22(x + -9)
(-18 + -72x + (2x + 8x2)) = -22(x + -9)

Combine like terms: -72x + 2x = -70x
(-18 + -70x + 8x2) = -22(x + -9)

Reorder the terms:
-18 + -70x + 8x2 = -22(-9 + x)
-18 + -70x + 8x2 = (-9 * -22 + x * -22)
-18 + -70x + 8x2 = (198 + -22x)

Solving
-18 + -70x + 8x2 = 198 + -22x

Solving for variable 'x'.

Reorder the terms:
-18 + -198 + -70x + 22x + 8x2 = 198 + -22x + -198 + 22x

Combine like terms: -18 + -198 = -216
-216 + -70x + 22x + 8x2 = 198 + -22x + -198 + 22x

Combine like terms: -70x + 22x = -48x
-216 + -48x + 8x2 = 198 + -22x + -198 + 22x

Reorder the terms:
-216 + -48x + 8x2 = 198 + -198 + -22x + 22x

Combine like terms: 198 + -198 = 0
-216 + -48x + 8x2 = 0 + -22x + 22x
-216 + -48x + 8x2 = -22x + 22x

Combine like terms: -22x + 22x = 0
-216 + -48x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-27 + -6x + x2) = 0

Factor a trinomial.
8((-3 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Solution

x = {-3, 9}

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