(4u+3)(4u+3)-(6u-3)(u+2)=2u(6+5u)+9

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Solution for (4u+3)(4u+3)-(6u-3)(u+2)=2u(6+5u)+9 equation: 


Simplifying
(4u + 3)(4u + 3) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9

Reorder the terms:
(3 + 4u)(4u + 3) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9

Reorder the terms:
(3 + 4u)(3 + 4u) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9

Multiply (3 + 4u) * (3 + 4u)
(3(3 + 4u) + 4u * (3 + 4u)) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9
((3 * 3 + 4u * 3) + 4u * (3 + 4u)) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9
((9 + 12u) + 4u * (3 + 4u)) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9
(9 + 12u + (3 * 4u + 4u * 4u)) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9
(9 + 12u + (12u + 16u2)) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9

Combine like terms: 12u + 12u = 24u
(9 + 24u + 16u2) + -1(6u + -3)(u + 2) = 2u(6 + 5u) + 9

Reorder the terms:
9 + 24u + 16u2 + -1(-3 + 6u)(u + 2) = 2u(6 + 5u) + 9

Reorder the terms:
9 + 24u + 16u2 + -1(-3 + 6u)(2 + u) = 2u(6 + 5u) + 9

Multiply (-3 + 6u) * (2 + u)
9 + 24u + 16u2 + -1(-3(2 + u) + 6u * (2 + u)) = 2u(6 + 5u) + 9
9 + 24u + 16u2 + -1((2 * -3 + u * -3) + 6u * (2 + u)) = 2u(6 + 5u) + 9
9 + 24u + 16u2 + -1((-6 + -3u) + 6u * (2 + u)) = 2u(6 + 5u) + 9
9 + 24u + 16u2 + -1(-6 + -3u + (2 * 6u + u * 6u)) = 2u(6 + 5u) + 9
9 + 24u + 16u2 + -1(-6 + -3u + (12u + 6u2)) = 2u(6 + 5u) + 9

Combine like terms: -3u + 12u = 9u
9 + 24u + 16u2 + -1(-6 + 9u + 6u2) = 2u(6 + 5u) + 9
9 + 24u + 16u2 + (-6 * -1 + 9u * -1 + 6u2 * -1) = 2u(6 + 5u) + 9
9 + 24u + 16u2 + (6 + -9u + -6u2) = 2u(6 + 5u) + 9

Reorder the terms:
9 + 6 + 24u + -9u + 16u2 + -6u2 = 2u(6 + 5u) + 9

Combine like terms: 9 + 6 = 15
15 + 24u + -9u + 16u2 + -6u2 = 2u(6 + 5u) + 9

Combine like terms: 24u + -9u = 15u
15 + 15u + 16u2 + -6u2 = 2u(6 + 5u) + 9

Combine like terms: 16u2 + -6u2 = 10u2
15 + 15u + 10u2 = 2u(6 + 5u) + 9
15 + 15u + 10u2 = (6 * 2u + 5u * 2u) + 9
15 + 15u + 10u2 = (12u + 10u2) + 9

Reorder the terms:
15 + 15u + 10u2 = 9 + 12u + 10u2

Add '-10u2' to each side of the equation.
15 + 15u + 10u2 + -10u2 = 9 + 12u + 10u2 + -10u2

Combine like terms: 10u2 + -10u2 = 0
15 + 15u + 0 = 9 + 12u + 10u2 + -10u2
15 + 15u = 9 + 12u + 10u2 + -10u2

Combine like terms: 10u2 + -10u2 = 0
15 + 15u = 9 + 12u + 0
15 + 15u = 9 + 12u

Solving
15 + 15u = 9 + 12u

Solving for variable 'u'.

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

Add '-12u' to each side of the equation.
15 + 15u + -12u = 9 + 12u + -12u

Combine like terms: 15u + -12u = 3u
15 + 3u = 9 + 12u + -12u

Combine like terms: 12u + -12u = 0
15 + 3u = 9 + 0
15 + 3u = 9

Add '-15' to each side of the equation.
15 + -15 + 3u = 9 + -15

Combine like terms: 15 + -15 = 0
0 + 3u = 9 + -15
3u = 9 + -15

Combine like terms: 9 + -15 = -6
3u = -6

Divide each side by '3'.
u = -2

Simplifying
u = -2

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