(2x+1)(3x-8)=(5x-24)(2x-5)-192

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Solution for (2x+1)(3x-8)=(5x-24)(2x-5)-192 equation:


Simplifying
(2x + 1)(3x + -8) = (5x + -24)(2x + -5) + -192

Reorder the terms:
(1 + 2x)(3x + -8) = (5x + -24)(2x + -5) + -192

Reorder the terms:
(1 + 2x)(-8 + 3x) = (5x + -24)(2x + -5) + -192

Multiply (1 + 2x) * (-8 + 3x)
(1(-8 + 3x) + 2x * (-8 + 3x)) = (5x + -24)(2x + -5) + -192
((-8 * 1 + 3x * 1) + 2x * (-8 + 3x)) = (5x + -24)(2x + -5) + -192
((-8 + 3x) + 2x * (-8 + 3x)) = (5x + -24)(2x + -5) + -192
(-8 + 3x + (-8 * 2x + 3x * 2x)) = (5x + -24)(2x + -5) + -192
(-8 + 3x + (-16x + 6x2)) = (5x + -24)(2x + -5) + -192

Combine like terms: 3x + -16x = -13x
(-8 + -13x + 6x2) = (5x + -24)(2x + -5) + -192

Reorder the terms:
-8 + -13x + 6x2 = (-24 + 5x)(2x + -5) + -192

Reorder the terms:
-8 + -13x + 6x2 = (-24 + 5x)(-5 + 2x) + -192

Multiply (-24 + 5x) * (-5 + 2x)
-8 + -13x + 6x2 = (-24(-5 + 2x) + 5x * (-5 + 2x)) + -192
-8 + -13x + 6x2 = ((-5 * -24 + 2x * -24) + 5x * (-5 + 2x)) + -192
-8 + -13x + 6x2 = ((120 + -48x) + 5x * (-5 + 2x)) + -192
-8 + -13x + 6x2 = (120 + -48x + (-5 * 5x + 2x * 5x)) + -192
-8 + -13x + 6x2 = (120 + -48x + (-25x + 10x2)) + -192

Combine like terms: -48x + -25x = -73x
-8 + -13x + 6x2 = (120 + -73x + 10x2) + -192

Reorder the terms:
-8 + -13x + 6x2 = 120 + -192 + -73x + 10x2

Combine like terms: 120 + -192 = -72
-8 + -13x + 6x2 = -72 + -73x + 10x2

Solving
-8 + -13x + 6x2 = -72 + -73x + 10x2

Solving for variable 'x'.

Reorder the terms:
-8 + 72 + -13x + 73x + 6x2 + -10x2 = -72 + -73x + 10x2 + 72 + 73x + -10x2

Combine like terms: -8 + 72 = 64
64 + -13x + 73x + 6x2 + -10x2 = -72 + -73x + 10x2 + 72 + 73x + -10x2

Combine like terms: -13x + 73x = 60x
64 + 60x + 6x2 + -10x2 = -72 + -73x + 10x2 + 72 + 73x + -10x2

Combine like terms: 6x2 + -10x2 = -4x2
64 + 60x + -4x2 = -72 + -73x + 10x2 + 72 + 73x + -10x2

Reorder the terms:
64 + 60x + -4x2 = -72 + 72 + -73x + 73x + 10x2 + -10x2

Combine like terms: -72 + 72 = 0
64 + 60x + -4x2 = 0 + -73x + 73x + 10x2 + -10x2
64 + 60x + -4x2 = -73x + 73x + 10x2 + -10x2

Combine like terms: -73x + 73x = 0
64 + 60x + -4x2 = 0 + 10x2 + -10x2
64 + 60x + -4x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
64 + 60x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + 15x + -1x2) = 0

Factor a trinomial.
4((16 + -1x)(1 + x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(16 + -1x)' equal to zero and attempt to solve: Simplifying 16 + -1x = 0 Solving 16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1x = 0 + -16 -1x = 0 + -16 Combine like terms: 0 + -16 = -16 -1x = -16 Divide each side by '-1'. x = 16 Simplifying x = 16

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {16, -1}

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