-(2x+11)(x-2)-(2x+11)(7x-1)=0

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Solution for -(2x+11)(x-2)-(2x+11)(7x-1)=0 equation:


Simplifying
-1(2x + 11)(x + -2) + -1(2x + 11)(7x + -1) = 0

Reorder the terms:
-1(11 + 2x)(x + -2) + -1(2x + 11)(7x + -1) = 0

Reorder the terms:
-1(11 + 2x)(-2 + x) + -1(2x + 11)(7x + -1) = 0

Multiply (11 + 2x) * (-2 + x)
-1(11(-2 + x) + 2x * (-2 + x)) + -1(2x + 11)(7x + -1) = 0
-1((-2 * 11 + x * 11) + 2x * (-2 + x)) + -1(2x + 11)(7x + -1) = 0
-1((-22 + 11x) + 2x * (-2 + x)) + -1(2x + 11)(7x + -1) = 0
-1(-22 + 11x + (-2 * 2x + x * 2x)) + -1(2x + 11)(7x + -1) = 0
-1(-22 + 11x + (-4x + 2x2)) + -1(2x + 11)(7x + -1) = 0

Combine like terms: 11x + -4x = 7x
-1(-22 + 7x + 2x2) + -1(2x + 11)(7x + -1) = 0
(-22 * -1 + 7x * -1 + 2x2 * -1) + -1(2x + 11)(7x + -1) = 0
(22 + -7x + -2x2) + -1(2x + 11)(7x + -1) = 0

Reorder the terms:
22 + -7x + -2x2 + -1(11 + 2x)(7x + -1) = 0

Reorder the terms:
22 + -7x + -2x2 + -1(11 + 2x)(-1 + 7x) = 0

Multiply (11 + 2x) * (-1 + 7x)
22 + -7x + -2x2 + -1(11(-1 + 7x) + 2x * (-1 + 7x)) = 0
22 + -7x + -2x2 + -1((-1 * 11 + 7x * 11) + 2x * (-1 + 7x)) = 0
22 + -7x + -2x2 + -1((-11 + 77x) + 2x * (-1 + 7x)) = 0
22 + -7x + -2x2 + -1(-11 + 77x + (-1 * 2x + 7x * 2x)) = 0
22 + -7x + -2x2 + -1(-11 + 77x + (-2x + 14x2)) = 0

Combine like terms: 77x + -2x = 75x
22 + -7x + -2x2 + -1(-11 + 75x + 14x2) = 0
22 + -7x + -2x2 + (-11 * -1 + 75x * -1 + 14x2 * -1) = 0
22 + -7x + -2x2 + (11 + -75x + -14x2) = 0

Reorder the terms:
22 + 11 + -7x + -75x + -2x2 + -14x2 = 0

Combine like terms: 22 + 11 = 33
33 + -7x + -75x + -2x2 + -14x2 = 0

Combine like terms: -7x + -75x = -82x
33 + -82x + -2x2 + -14x2 = 0

Combine like terms: -2x2 + -14x2 = -16x2
33 + -82x + -16x2 = 0

Solving
33 + -82x + -16x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -8x)(11 + 2x) = 0

Subproblem 1

Set the factor '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 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 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375

Subproblem 2

Set the factor '(11 + 2x)' equal to zero and attempt to solve: Simplifying 11 + 2x = 0 Solving 11 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 2x = 0 + -11 2x = 0 + -11 Combine like terms: 0 + -11 = -11 2x = -11 Divide each side by '2'. x = -5.5 Simplifying x = -5.5

Solution

x = {0.375, -5.5}

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