(x+6)(4x-3)=(2x+3)(2x+3)

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Solution for (x+6)(4x-3)=(2x+3)(2x+3) equation: 


Simplifying
(x + 6)(4x + -3) = (2x + 3)(2x + 3)

Reorder the terms:
(6 + x)(4x + -3) = (2x + 3)(2x + 3)

Reorder the terms:
(6 + x)(-3 + 4x) = (2x + 3)(2x + 3)

Multiply (6 + x) * (-3 + 4x)
(6(-3 + 4x) + x(-3 + 4x)) = (2x + 3)(2x + 3)
((-3 * 6 + 4x * 6) + x(-3 + 4x)) = (2x + 3)(2x + 3)
((-18 + 24x) + x(-3 + 4x)) = (2x + 3)(2x + 3)
(-18 + 24x + (-3 * x + 4x * x)) = (2x + 3)(2x + 3)
(-18 + 24x + (-3x + 4x2)) = (2x + 3)(2x + 3)

Combine like terms: 24x + -3x = 21x
(-18 + 21x + 4x2) = (2x + 3)(2x + 3)

Reorder the terms:
-18 + 21x + 4x2 = (3 + 2x)(2x + 3)

Reorder the terms:
-18 + 21x + 4x2 = (3 + 2x)(3 + 2x)

Multiply (3 + 2x) * (3 + 2x)
-18 + 21x + 4x2 = (3(3 + 2x) + 2x * (3 + 2x))
-18 + 21x + 4x2 = ((3 * 3 + 2x * 3) + 2x * (3 + 2x))
-18 + 21x + 4x2 = ((9 + 6x) + 2x * (3 + 2x))
-18 + 21x + 4x2 = (9 + 6x + (3 * 2x + 2x * 2x))
-18 + 21x + 4x2 = (9 + 6x + (6x + 4x2))

Combine like terms: 6x + 6x = 12x
-18 + 21x + 4x2 = (9 + 12x + 4x2)

Add '-4x2' to each side of the equation.
-18 + 21x + 4x2 + -4x2 = 9 + 12x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-18 + 21x + 0 = 9 + 12x + 4x2 + -4x2
-18 + 21x = 9 + 12x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-18 + 21x = 9 + 12x + 0
-18 + 21x = 9 + 12x

Solving
-18 + 21x = 9 + 12x

Solving for variable 'x'.

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

Add '-12x' to each side of the equation.
-18 + 21x + -12x = 9 + 12x + -12x

Combine like terms: 21x + -12x = 9x
-18 + 9x = 9 + 12x + -12x

Combine like terms: 12x + -12x = 0
-18 + 9x = 9 + 0
-18 + 9x = 9

Add '18' to each side of the equation.
-18 + 18 + 9x = 9 + 18

Combine like terms: -18 + 18 = 0
0 + 9x = 9 + 18
9x = 9 + 18

Combine like terms: 9 + 18 = 27
9x = 27

Divide each side by '9'.
x = 3

Simplifying
x = 3

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