(3x+4)(3x+4)=(5x-4)(5x-4)

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Solution for (3x+4)(3x+4)=(5x-4)(5x-4) equation: 


Simplifying
(3x + 4)(3x + 4) = (5x + -4)(5x + -4)

Reorder the terms:
(4 + 3x)(3x + 4) = (5x + -4)(5x + -4)

Reorder the terms:
(4 + 3x)(4 + 3x) = (5x + -4)(5x + -4)

Multiply (4 + 3x) * (4 + 3x)
(4(4 + 3x) + 3x * (4 + 3x)) = (5x + -4)(5x + -4)
((4 * 4 + 3x * 4) + 3x * (4 + 3x)) = (5x + -4)(5x + -4)
((16 + 12x) + 3x * (4 + 3x)) = (5x + -4)(5x + -4)
(16 + 12x + (4 * 3x + 3x * 3x)) = (5x + -4)(5x + -4)
(16 + 12x + (12x + 9x2)) = (5x + -4)(5x + -4)

Combine like terms: 12x + 12x = 24x
(16 + 24x + 9x2) = (5x + -4)(5x + -4)

Reorder the terms:
16 + 24x + 9x2 = (-4 + 5x)(5x + -4)

Reorder the terms:
16 + 24x + 9x2 = (-4 + 5x)(-4 + 5x)

Multiply (-4 + 5x) * (-4 + 5x)
16 + 24x + 9x2 = (-4(-4 + 5x) + 5x * (-4 + 5x))
16 + 24x + 9x2 = ((-4 * -4 + 5x * -4) + 5x * (-4 + 5x))
16 + 24x + 9x2 = ((16 + -20x) + 5x * (-4 + 5x))
16 + 24x + 9x2 = (16 + -20x + (-4 * 5x + 5x * 5x))
16 + 24x + 9x2 = (16 + -20x + (-20x + 25x2))

Combine like terms: -20x + -20x = -40x
16 + 24x + 9x2 = (16 + -40x + 25x2)

Add '-16' to each side of the equation.
16 + 24x + -16 + 9x2 = 16 + -40x + -16 + 25x2

Reorder the terms:
16 + -16 + 24x + 9x2 = 16 + -40x + -16 + 25x2

Combine like terms: 16 + -16 = 0
0 + 24x + 9x2 = 16 + -40x + -16 + 25x2
24x + 9x2 = 16 + -40x + -16 + 25x2

Reorder the terms:
24x + 9x2 = 16 + -16 + -40x + 25x2

Combine like terms: 16 + -16 = 0
24x + 9x2 = 0 + -40x + 25x2
24x + 9x2 = -40x + 25x2

Solving
24x + 9x2 = -40x + 25x2

Solving for variable 'x'.

Reorder the terms:
24x + 40x + 9x2 + -25x2 = -40x + 25x2 + 40x + -25x2

Combine like terms: 24x + 40x = 64x
64x + 9x2 + -25x2 = -40x + 25x2 + 40x + -25x2

Combine like terms: 9x2 + -25x2 = -16x2
64x + -16x2 = -40x + 25x2 + 40x + -25x2

Reorder the terms:
64x + -16x2 = -40x + 40x + 25x2 + -25x2

Combine like terms: -40x + 40x = 0
64x + -16x2 = 0 + 25x2 + -25x2
64x + -16x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
64x + -16x2 = 0

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

Ignore the factor 16.

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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 4}

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