(2x+1)(2x+6)-7(x-2)=4(x+1)(x-1)-9x

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Solution for (2x+1)(2x+6)-7(x-2)=4(x+1)(x-1)-9x equation:


Simplifying
(2x + 1)(2x + 6) + -7(x + -2) = 4(x + 1)(x + -1) + -9x

Reorder the terms:
(1 + 2x)(2x + 6) + -7(x + -2) = 4(x + 1)(x + -1) + -9x

Reorder the terms:
(1 + 2x)(6 + 2x) + -7(x + -2) = 4(x + 1)(x + -1) + -9x

Multiply (1 + 2x) * (6 + 2x)
(1(6 + 2x) + 2x * (6 + 2x)) + -7(x + -2) = 4(x + 1)(x + -1) + -9x
((6 * 1 + 2x * 1) + 2x * (6 + 2x)) + -7(x + -2) = 4(x + 1)(x + -1) + -9x
((6 + 2x) + 2x * (6 + 2x)) + -7(x + -2) = 4(x + 1)(x + -1) + -9x
(6 + 2x + (6 * 2x + 2x * 2x)) + -7(x + -2) = 4(x + 1)(x + -1) + -9x
(6 + 2x + (12x + 4x2)) + -7(x + -2) = 4(x + 1)(x + -1) + -9x

Combine like terms: 2x + 12x = 14x
(6 + 14x + 4x2) + -7(x + -2) = 4(x + 1)(x + -1) + -9x

Reorder the terms:
6 + 14x + 4x2 + -7(-2 + x) = 4(x + 1)(x + -1) + -9x
6 + 14x + 4x2 + (-2 * -7 + x * -7) = 4(x + 1)(x + -1) + -9x
6 + 14x + 4x2 + (14 + -7x) = 4(x + 1)(x + -1) + -9x

Reorder the terms:
6 + 14 + 14x + -7x + 4x2 = 4(x + 1)(x + -1) + -9x

Combine like terms: 6 + 14 = 20
20 + 14x + -7x + 4x2 = 4(x + 1)(x + -1) + -9x

Combine like terms: 14x + -7x = 7x
20 + 7x + 4x2 = 4(x + 1)(x + -1) + -9x

Reorder the terms:
20 + 7x + 4x2 = 4(1 + x)(x + -1) + -9x

Reorder the terms:
20 + 7x + 4x2 = 4(1 + x)(-1 + x) + -9x

Multiply (1 + x) * (-1 + x)
20 + 7x + 4x2 = 4(1(-1 + x) + x(-1 + x)) + -9x
20 + 7x + 4x2 = 4((-1 * 1 + x * 1) + x(-1 + x)) + -9x
20 + 7x + 4x2 = 4((-1 + 1x) + x(-1 + x)) + -9x
20 + 7x + 4x2 = 4(-1 + 1x + (-1 * x + x * x)) + -9x
20 + 7x + 4x2 = 4(-1 + 1x + (-1x + x2)) + -9x

Combine like terms: 1x + -1x = 0
20 + 7x + 4x2 = 4(-1 + 0 + x2) + -9x
20 + 7x + 4x2 = 4(-1 + x2) + -9x
20 + 7x + 4x2 = (-1 * 4 + x2 * 4) + -9x
20 + 7x + 4x2 = (-4 + 4x2) + -9x

Reorder the terms:
20 + 7x + 4x2 = -4 + -9x + 4x2

Add '-4x2' to each side of the equation.
20 + 7x + 4x2 + -4x2 = -4 + -9x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
20 + 7x + 0 = -4 + -9x + 4x2 + -4x2
20 + 7x = -4 + -9x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
20 + 7x = -4 + -9x + 0
20 + 7x = -4 + -9x

Solving
20 + 7x = -4 + -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.
20 + 7x + 9x = -4 + -9x + 9x

Combine like terms: 7x + 9x = 16x
20 + 16x = -4 + -9x + 9x

Combine like terms: -9x + 9x = 0
20 + 16x = -4 + 0
20 + 16x = -4

Add '-20' to each side of the equation.
20 + -20 + 16x = -4 + -20

Combine like terms: 20 + -20 = 0
0 + 16x = -4 + -20
16x = -4 + -20

Combine like terms: -4 + -20 = -24
16x = -24

Divide each side by '16'.
x = -1.5

Simplifying
x = -1.5

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