(5-6x)(4x+11)-(3x+7)(5-6x)=0

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Solution for (5-6x)(4x+11)-(3x+7)(5-6x)=0 equation: 


Simplifying
(5 + -6x)(4x + 11) + -1(3x + 7)(5 + -6x) = 0

Reorder the terms:
(5 + -6x)(11 + 4x) + -1(3x + 7)(5 + -6x) = 0

Multiply (5 + -6x) * (11 + 4x)
(5(11 + 4x) + -6x * (11 + 4x)) + -1(3x + 7)(5 + -6x) = 0
((11 * 5 + 4x * 5) + -6x * (11 + 4x)) + -1(3x + 7)(5 + -6x) = 0
((55 + 20x) + -6x * (11 + 4x)) + -1(3x + 7)(5 + -6x) = 0
(55 + 20x + (11 * -6x + 4x * -6x)) + -1(3x + 7)(5 + -6x) = 0
(55 + 20x + (-66x + -24x2)) + -1(3x + 7)(5 + -6x) = 0

Combine like terms: 20x + -66x = -46x
(55 + -46x + -24x2) + -1(3x + 7)(5 + -6x) = 0

Reorder the terms:
55 + -46x + -24x2 + -1(7 + 3x)(5 + -6x) = 0

Multiply (7 + 3x) * (5 + -6x)
55 + -46x + -24x2 + -1(7(5 + -6x) + 3x * (5 + -6x)) = 0
55 + -46x + -24x2 + -1((5 * 7 + -6x * 7) + 3x * (5 + -6x)) = 0
55 + -46x + -24x2 + -1((35 + -42x) + 3x * (5 + -6x)) = 0
55 + -46x + -24x2 + -1(35 + -42x + (5 * 3x + -6x * 3x)) = 0
55 + -46x + -24x2 + -1(35 + -42x + (15x + -18x2)) = 0

Combine like terms: -42x + 15x = -27x
55 + -46x + -24x2 + -1(35 + -27x + -18x2) = 0
55 + -46x + -24x2 + (35 * -1 + -27x * -1 + -18x2 * -1) = 0
55 + -46x + -24x2 + (-35 + 27x + 18x2) = 0

Reorder the terms:
55 + -35 + -46x + 27x + -24x2 + 18x2 = 0

Combine like terms: 55 + -35 = 20
20 + -46x + 27x + -24x2 + 18x2 = 0

Combine like terms: -46x + 27x = -19x
20 + -19x + -24x2 + 18x2 = 0

Combine like terms: -24x2 + 18x2 = -6x2
20 + -19x + -6x2 = 0

Solving
20 + -19x + -6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -6x)(4 + x) = 0


Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {0.8333333333, -4}

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