(24)(45)=(2x-8)(x+8)

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Solution for (24)(45)=(2x-8)(x+8) equation: 


Simplifying
(24)(45) = (2x + -8)(x + 8)

Multiply 24 * 45
1080 = (2x + -8)(x + 8)

Reorder the terms:
1080 = (-8 + 2x)(x + 8)

Reorder the terms:
1080 = (-8 + 2x)(8 + x)

Multiply (-8 + 2x) * (8 + x)
1080 = (-8(8 + x) + 2x * (8 + x))
1080 = ((8 * -8 + x * -8) + 2x * (8 + x))
1080 = ((-64 + -8x) + 2x * (8 + x))
1080 = (-64 + -8x + (8 * 2x + x * 2x))
1080 = (-64 + -8x + (16x + 2x2))

Combine like terms: -8x + 16x = 8x
1080 = (-64 + 8x + 2x2)

Solving
1080 = -64 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 1080 + 64 = 1144
1144 + -8x + -2x2 = -64 + 8x + 2x2 + 64 + -8x + -2x2

Reorder the terms:
1144 + -8x + -2x2 = -64 + 64 + 8x + -8x + 2x2 + -2x2

Combine like terms: -64 + 64 = 0
1144 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
1144 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
1144 + -8x + -2x2 = 0 + 2x2 + -2x2
1144 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1144 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(572 + -4x + -1x2) = 0

Factor a trinomial.
2((22 + -1x)(26 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22

Subproblem 2
Set the factor '(26 + x)' equal to zero and attempt to solve:

Simplifying
26 + x = 0

Solving
26 + x = 0

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

Add '-26' to each side of the equation.
26 + -26 + x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + x = 0 + -26
x = 0 + -26

Combine like terms: 0 + -26 = -26
x = -26

Simplifying
x = -26
Solution
x = {22, -26}

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