(3x+5)*(3x+5)-(2x-7)*(2x-7)=24(2x-1)

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Solution for (3x+5)*(3x+5)-(2x-7)*(2x-7)=24(2x-1) equation:


Simplifying
(3x + 5)(3x + 5) + -1(2x + -7)(2x + -7) = 24(2x + -1)

Reorder the terms:
(5 + 3x)(3x + 5) + -1(2x + -7)(2x + -7) = 24(2x + -1)

Reorder the terms:
(5 + 3x)(5 + 3x) + -1(2x + -7)(2x + -7) = 24(2x + -1)

Multiply (5 + 3x) * (5 + 3x)
(5(5 + 3x) + 3x * (5 + 3x)) + -1(2x + -7)(2x + -7) = 24(2x + -1)
((5 * 5 + 3x * 5) + 3x * (5 + 3x)) + -1(2x + -7)(2x + -7) = 24(2x + -1)
((25 + 15x) + 3x * (5 + 3x)) + -1(2x + -7)(2x + -7) = 24(2x + -1)
(25 + 15x + (5 * 3x + 3x * 3x)) + -1(2x + -7)(2x + -7) = 24(2x + -1)
(25 + 15x + (15x + 9x2)) + -1(2x + -7)(2x + -7) = 24(2x + -1)

Combine like terms: 15x + 15x = 30x
(25 + 30x + 9x2) + -1(2x + -7)(2x + -7) = 24(2x + -1)

Reorder the terms:
25 + 30x + 9x2 + -1(-7 + 2x)(2x + -7) = 24(2x + -1)

Reorder the terms:
25 + 30x + 9x2 + -1(-7 + 2x)(-7 + 2x) = 24(2x + -1)

Multiply (-7 + 2x) * (-7 + 2x)
25 + 30x + 9x2 + -1(-7(-7 + 2x) + 2x * (-7 + 2x)) = 24(2x + -1)
25 + 30x + 9x2 + -1((-7 * -7 + 2x * -7) + 2x * (-7 + 2x)) = 24(2x + -1)
25 + 30x + 9x2 + -1((49 + -14x) + 2x * (-7 + 2x)) = 24(2x + -1)
25 + 30x + 9x2 + -1(49 + -14x + (-7 * 2x + 2x * 2x)) = 24(2x + -1)
25 + 30x + 9x2 + -1(49 + -14x + (-14x + 4x2)) = 24(2x + -1)

Combine like terms: -14x + -14x = -28x
25 + 30x + 9x2 + -1(49 + -28x + 4x2) = 24(2x + -1)
25 + 30x + 9x2 + (49 * -1 + -28x * -1 + 4x2 * -1) = 24(2x + -1)
25 + 30x + 9x2 + (-49 + 28x + -4x2) = 24(2x + -1)

Reorder the terms:
25 + -49 + 30x + 28x + 9x2 + -4x2 = 24(2x + -1)

Combine like terms: 25 + -49 = -24
-24 + 30x + 28x + 9x2 + -4x2 = 24(2x + -1)

Combine like terms: 30x + 28x = 58x
-24 + 58x + 9x2 + -4x2 = 24(2x + -1)

Combine like terms: 9x2 + -4x2 = 5x2
-24 + 58x + 5x2 = 24(2x + -1)

Reorder the terms:
-24 + 58x + 5x2 = 24(-1 + 2x)
-24 + 58x + 5x2 = (-1 * 24 + 2x * 24)
-24 + 58x + 5x2 = (-24 + 48x)

Add '24' to each side of the equation.
-24 + 58x + 24 + 5x2 = -24 + 24 + 48x

Reorder the terms:
-24 + 24 + 58x + 5x2 = -24 + 24 + 48x

Combine like terms: -24 + 24 = 0
0 + 58x + 5x2 = -24 + 24 + 48x
58x + 5x2 = -24 + 24 + 48x

Combine like terms: -24 + 24 = 0
58x + 5x2 = 0 + 48x
58x + 5x2 = 48x

Solving
58x + 5x2 = 48x

Solving for variable 'x'.

Reorder the terms:
58x + -48x + 5x2 = 48x + -48x

Combine like terms: 58x + -48x = 10x
10x + 5x2 = 48x + -48x

Combine like terms: 48x + -48x = 0
10x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(2 + x) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {0, -2}

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