(3x+7)(3x+7)-(2x-3)(2x-3)=0

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Solution for (3x+7)(3x+7)-(2x-3)(2x-3)=0 equation:


Simplifying
(3x + 7)(3x + 7) + -1(2x + -3)(2x + -3) = 0

Reorder the terms:
(7 + 3x)(3x + 7) + -1(2x + -3)(2x + -3) = 0

Reorder the terms:
(7 + 3x)(7 + 3x) + -1(2x + -3)(2x + -3) = 0

Multiply (7 + 3x) * (7 + 3x)
(7(7 + 3x) + 3x * (7 + 3x)) + -1(2x + -3)(2x + -3) = 0
((7 * 7 + 3x * 7) + 3x * (7 + 3x)) + -1(2x + -3)(2x + -3) = 0
((49 + 21x) + 3x * (7 + 3x)) + -1(2x + -3)(2x + -3) = 0
(49 + 21x + (7 * 3x + 3x * 3x)) + -1(2x + -3)(2x + -3) = 0
(49 + 21x + (21x + 9x2)) + -1(2x + -3)(2x + -3) = 0

Combine like terms: 21x + 21x = 42x
(49 + 42x + 9x2) + -1(2x + -3)(2x + -3) = 0

Reorder the terms:
49 + 42x + 9x2 + -1(-3 + 2x)(2x + -3) = 0

Reorder the terms:
49 + 42x + 9x2 + -1(-3 + 2x)(-3 + 2x) = 0

Multiply (-3 + 2x) * (-3 + 2x)
49 + 42x + 9x2 + -1(-3(-3 + 2x) + 2x * (-3 + 2x)) = 0
49 + 42x + 9x2 + -1((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 0
49 + 42x + 9x2 + -1((9 + -6x) + 2x * (-3 + 2x)) = 0
49 + 42x + 9x2 + -1(9 + -6x + (-3 * 2x + 2x * 2x)) = 0
49 + 42x + 9x2 + -1(9 + -6x + (-6x + 4x2)) = 0

Combine like terms: -6x + -6x = -12x
49 + 42x + 9x2 + -1(9 + -12x + 4x2) = 0
49 + 42x + 9x2 + (9 * -1 + -12x * -1 + 4x2 * -1) = 0
49 + 42x + 9x2 + (-9 + 12x + -4x2) = 0

Reorder the terms:
49 + -9 + 42x + 12x + 9x2 + -4x2 = 0

Combine like terms: 49 + -9 = 40
40 + 42x + 12x + 9x2 + -4x2 = 0

Combine like terms: 42x + 12x = 54x
40 + 54x + 9x2 + -4x2 = 0

Combine like terms: 9x2 + -4x2 = 5x2
40 + 54x + 5x2 = 0

Solving
40 + 54x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + x)(4 + 5x) = 0

Subproblem 1

Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10

Subproblem 2

Set the factor '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Divide each side by '5'. x = -0.8 Simplifying x = -0.8

Solution

x = {-10, -0.8}

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