(x+12)(4x+1)=(2x+7)(2x+9)

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Solution for (x+12)(4x+1)=(2x+7)(2x+9) equation: 


Simplifying
(x + 12)(4x + 1) = (2x + 7)(2x + 9)

Reorder the terms:
(12 + x)(4x + 1) = (2x + 7)(2x + 9)

Reorder the terms:
(12 + x)(1 + 4x) = (2x + 7)(2x + 9)

Multiply (12 + x) * (1 + 4x)
(12(1 + 4x) + x(1 + 4x)) = (2x + 7)(2x + 9)
((1 * 12 + 4x * 12) + x(1 + 4x)) = (2x + 7)(2x + 9)
((12 + 48x) + x(1 + 4x)) = (2x + 7)(2x + 9)
(12 + 48x + (1 * x + 4x * x)) = (2x + 7)(2x + 9)
(12 + 48x + (1x + 4x2)) = (2x + 7)(2x + 9)

Combine like terms: 48x + 1x = 49x
(12 + 49x + 4x2) = (2x + 7)(2x + 9)

Reorder the terms:
12 + 49x + 4x2 = (7 + 2x)(2x + 9)

Reorder the terms:
12 + 49x + 4x2 = (7 + 2x)(9 + 2x)

Multiply (7 + 2x) * (9 + 2x)
12 + 49x + 4x2 = (7(9 + 2x) + 2x * (9 + 2x))
12 + 49x + 4x2 = ((9 * 7 + 2x * 7) + 2x * (9 + 2x))
12 + 49x + 4x2 = ((63 + 14x) + 2x * (9 + 2x))
12 + 49x + 4x2 = (63 + 14x + (9 * 2x + 2x * 2x))
12 + 49x + 4x2 = (63 + 14x + (18x + 4x2))

Combine like terms: 14x + 18x = 32x
12 + 49x + 4x2 = (63 + 32x + 4x2)

Add '-4x2' to each side of the equation.
12 + 49x + 4x2 + -4x2 = 63 + 32x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + 49x + 0 = 63 + 32x + 4x2 + -4x2
12 + 49x = 63 + 32x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + 49x = 63 + 32x + 0
12 + 49x = 63 + 32x

Solving
12 + 49x = 63 + 32x

Solving for variable 'x'.

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

Add '-32x' to each side of the equation.
12 + 49x + -32x = 63 + 32x + -32x

Combine like terms: 49x + -32x = 17x
12 + 17x = 63 + 32x + -32x

Combine like terms: 32x + -32x = 0
12 + 17x = 63 + 0
12 + 17x = 63

Add '-12' to each side of the equation.
12 + -12 + 17x = 63 + -12

Combine like terms: 12 + -12 = 0
0 + 17x = 63 + -12
17x = 63 + -12

Combine like terms: 63 + -12 = 51
17x = 51

Divide each side by '17'.
x = 3

Simplifying
x = 3

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