(3x+4)(4x+1)-(2x+3)(x+3)=(5x+2)(2x+1)

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Solution for (3x+4)(4x+1)-(2x+3)(x+3)=(5x+2)(2x+1) equation:


Simplifying
(3x + 4)(4x + 1) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)

Reorder the terms:
(4 + 3x)(4x + 1) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)

Reorder the terms:
(4 + 3x)(1 + 4x) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)

Multiply (4 + 3x) * (1 + 4x)
(4(1 + 4x) + 3x * (1 + 4x)) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)
((1 * 4 + 4x * 4) + 3x * (1 + 4x)) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)
((4 + 16x) + 3x * (1 + 4x)) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)
(4 + 16x + (1 * 3x + 4x * 3x)) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)
(4 + 16x + (3x + 12x2)) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)

Combine like terms: 16x + 3x = 19x
(4 + 19x + 12x2) + -1(2x + 3)(x + 3) = (5x + 2)(2x + 1)

Reorder the terms:
4 + 19x + 12x2 + -1(3 + 2x)(x + 3) = (5x + 2)(2x + 1)

Reorder the terms:
4 + 19x + 12x2 + -1(3 + 2x)(3 + x) = (5x + 2)(2x + 1)

Multiply (3 + 2x) * (3 + x)
4 + 19x + 12x2 + -1(3(3 + x) + 2x * (3 + x)) = (5x + 2)(2x + 1)
4 + 19x + 12x2 + -1((3 * 3 + x * 3) + 2x * (3 + x)) = (5x + 2)(2x + 1)
4 + 19x + 12x2 + -1((9 + 3x) + 2x * (3 + x)) = (5x + 2)(2x + 1)
4 + 19x + 12x2 + -1(9 + 3x + (3 * 2x + x * 2x)) = (5x + 2)(2x + 1)
4 + 19x + 12x2 + -1(9 + 3x + (6x + 2x2)) = (5x + 2)(2x + 1)

Combine like terms: 3x + 6x = 9x
4 + 19x + 12x2 + -1(9 + 9x + 2x2) = (5x + 2)(2x + 1)
4 + 19x + 12x2 + (9 * -1 + 9x * -1 + 2x2 * -1) = (5x + 2)(2x + 1)
4 + 19x + 12x2 + (-9 + -9x + -2x2) = (5x + 2)(2x + 1)

Reorder the terms:
4 + -9 + 19x + -9x + 12x2 + -2x2 = (5x + 2)(2x + 1)

Combine like terms: 4 + -9 = -5
-5 + 19x + -9x + 12x2 + -2x2 = (5x + 2)(2x + 1)

Combine like terms: 19x + -9x = 10x
-5 + 10x + 12x2 + -2x2 = (5x + 2)(2x + 1)

Combine like terms: 12x2 + -2x2 = 10x2
-5 + 10x + 10x2 = (5x + 2)(2x + 1)

Reorder the terms:
-5 + 10x + 10x2 = (2 + 5x)(2x + 1)

Reorder the terms:
-5 + 10x + 10x2 = (2 + 5x)(1 + 2x)

Multiply (2 + 5x) * (1 + 2x)
-5 + 10x + 10x2 = (2(1 + 2x) + 5x * (1 + 2x))
-5 + 10x + 10x2 = ((1 * 2 + 2x * 2) + 5x * (1 + 2x))
-5 + 10x + 10x2 = ((2 + 4x) + 5x * (1 + 2x))
-5 + 10x + 10x2 = (2 + 4x + (1 * 5x + 2x * 5x))
-5 + 10x + 10x2 = (2 + 4x + (5x + 10x2))

Combine like terms: 4x + 5x = 9x
-5 + 10x + 10x2 = (2 + 9x + 10x2)

Add '-10x2' to each side of the equation.
-5 + 10x + 10x2 + -10x2 = 2 + 9x + 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-5 + 10x + 0 = 2 + 9x + 10x2 + -10x2
-5 + 10x = 2 + 9x + 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-5 + 10x = 2 + 9x + 0
-5 + 10x = 2 + 9x

Solving
-5 + 10x = 2 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
-5 + 10x + -9x = 2 + 9x + -9x

Combine like terms: 10x + -9x = 1x
-5 + 1x = 2 + 9x + -9x

Combine like terms: 9x + -9x = 0
-5 + 1x = 2 + 0
-5 + 1x = 2

Add '5' to each side of the equation.
-5 + 5 + 1x = 2 + 5

Combine like terms: -5 + 5 = 0
0 + 1x = 2 + 5
1x = 2 + 5

Combine like terms: 2 + 5 = 7
1x = 7

Divide each side by '1'.
x = 7

Simplifying
x = 7

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