(6x+11)(x-3)=(5x+9)(x-4)

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Solution for (6x+11)(x-3)=(5x+9)(x-4) equation:


Simplifying
(6x + 11)(x + -3) = (5x + 9)(x + -4)

Reorder the terms:
(11 + 6x)(x + -3) = (5x + 9)(x + -4)

Reorder the terms:
(11 + 6x)(-3 + x) = (5x + 9)(x + -4)

Multiply (11 + 6x) * (-3 + x)
(11(-3 + x) + 6x * (-3 + x)) = (5x + 9)(x + -4)
((-3 * 11 + x * 11) + 6x * (-3 + x)) = (5x + 9)(x + -4)
((-33 + 11x) + 6x * (-3 + x)) = (5x + 9)(x + -4)
(-33 + 11x + (-3 * 6x + x * 6x)) = (5x + 9)(x + -4)
(-33 + 11x + (-18x + 6x2)) = (5x + 9)(x + -4)

Combine like terms: 11x + -18x = -7x
(-33 + -7x + 6x2) = (5x + 9)(x + -4)

Reorder the terms:
-33 + -7x + 6x2 = (9 + 5x)(x + -4)

Reorder the terms:
-33 + -7x + 6x2 = (9 + 5x)(-4 + x)

Multiply (9 + 5x) * (-4 + x)
-33 + -7x + 6x2 = (9(-4 + x) + 5x * (-4 + x))
-33 + -7x + 6x2 = ((-4 * 9 + x * 9) + 5x * (-4 + x))
-33 + -7x + 6x2 = ((-36 + 9x) + 5x * (-4 + x))
-33 + -7x + 6x2 = (-36 + 9x + (-4 * 5x + x * 5x))
-33 + -7x + 6x2 = (-36 + 9x + (-20x + 5x2))

Combine like terms: 9x + -20x = -11x
-33 + -7x + 6x2 = (-36 + -11x + 5x2)

Solving
-33 + -7x + 6x2 = -36 + -11x + 5x2

Solving for variable 'x'.

Reorder the terms:
-33 + 36 + -7x + 11x + 6x2 + -5x2 = -36 + -11x + 5x2 + 36 + 11x + -5x2

Combine like terms: -33 + 36 = 3
3 + -7x + 11x + 6x2 + -5x2 = -36 + -11x + 5x2 + 36 + 11x + -5x2

Combine like terms: -7x + 11x = 4x
3 + 4x + 6x2 + -5x2 = -36 + -11x + 5x2 + 36 + 11x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
3 + 4x + 1x2 = -36 + -11x + 5x2 + 36 + 11x + -5x2

Reorder the terms:
3 + 4x + 1x2 = -36 + 36 + -11x + 11x + 5x2 + -5x2

Combine like terms: -36 + 36 = 0
3 + 4x + 1x2 = 0 + -11x + 11x + 5x2 + -5x2
3 + 4x + 1x2 = -11x + 11x + 5x2 + -5x2

Combine like terms: -11x + 11x = 0
3 + 4x + 1x2 = 0 + 5x2 + -5x2
3 + 4x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
3 + 4x + 1x2 = 0

Factor a trinomial.
(3 + x)(1 + x) = 0

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-3, -1}

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