(2*x-3)*(2*x-3)+6*x=(4*x+1)(x-2)-17

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Solution for (2*x-3)*(2*x-3)+6*x=(4*x+1)(x-2)-17 equation:


Simplifying
(2x + -3)(2x + -3) + 6x = (4x + 1)(x + -2) + -17

Reorder the terms:
(-3 + 2x)(2x + -3) + 6x = (4x + 1)(x + -2) + -17

Reorder the terms:
(-3 + 2x)(-3 + 2x) + 6x = (4x + 1)(x + -2) + -17

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) + 6x = (4x + 1)(x + -2) + -17
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + 6x = (4x + 1)(x + -2) + -17
((9 + -6x) + 2x * (-3 + 2x)) + 6x = (4x + 1)(x + -2) + -17
(9 + -6x + (-3 * 2x + 2x * 2x)) + 6x = (4x + 1)(x + -2) + -17
(9 + -6x + (-6x + 4x2)) + 6x = (4x + 1)(x + -2) + -17

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) + 6x = (4x + 1)(x + -2) + -17

Reorder the terms:
9 + -12x + 6x + 4x2 = (4x + 1)(x + -2) + -17

Combine like terms: -12x + 6x = -6x
9 + -6x + 4x2 = (4x + 1)(x + -2) + -17

Reorder the terms:
9 + -6x + 4x2 = (1 + 4x)(x + -2) + -17

Reorder the terms:
9 + -6x + 4x2 = (1 + 4x)(-2 + x) + -17

Multiply (1 + 4x) * (-2 + x)
9 + -6x + 4x2 = (1(-2 + x) + 4x * (-2 + x)) + -17
9 + -6x + 4x2 = ((-2 * 1 + x * 1) + 4x * (-2 + x)) + -17
9 + -6x + 4x2 = ((-2 + 1x) + 4x * (-2 + x)) + -17
9 + -6x + 4x2 = (-2 + 1x + (-2 * 4x + x * 4x)) + -17
9 + -6x + 4x2 = (-2 + 1x + (-8x + 4x2)) + -17

Combine like terms: 1x + -8x = -7x
9 + -6x + 4x2 = (-2 + -7x + 4x2) + -17

Reorder the terms:
9 + -6x + 4x2 = -2 + -17 + -7x + 4x2

Combine like terms: -2 + -17 = -19
9 + -6x + 4x2 = -19 + -7x + 4x2

Add '-4x2' to each side of the equation.
9 + -6x + 4x2 + -4x2 = -19 + -7x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + -6x + 0 = -19 + -7x + 4x2 + -4x2
9 + -6x = -19 + -7x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + -6x = -19 + -7x + 0
9 + -6x = -19 + -7x

Solving
9 + -6x = -19 + -7x

Solving for variable 'x'.

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

Add '7x' to each side of the equation.
9 + -6x + 7x = -19 + -7x + 7x

Combine like terms: -6x + 7x = 1x
9 + 1x = -19 + -7x + 7x

Combine like terms: -7x + 7x = 0
9 + 1x = -19 + 0
9 + 1x = -19

Add '-9' to each side of the equation.
9 + -9 + 1x = -19 + -9

Combine like terms: 9 + -9 = 0
0 + 1x = -19 + -9
1x = -19 + -9

Combine like terms: -19 + -9 = -28
1x = -28

Divide each side by '1'.
x = -28

Simplifying
x = -28

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