(7x+8)(2x-11)=0

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Solution for (7x+8)(2x-11)=0 equation: 


Simplifying
(7x + 8)(2x + -11) = 0

Reorder the terms:
(8 + 7x)(2x + -11) = 0

Reorder the terms:
(8 + 7x)(-11 + 2x) = 0

Multiply (8 + 7x) * (-11 + 2x)
(8(-11 + 2x) + 7x * (-11 + 2x)) = 0
((-11 * 8 + 2x * 8) + 7x * (-11 + 2x)) = 0
((-88 + 16x) + 7x * (-11 + 2x)) = 0
(-88 + 16x + (-11 * 7x + 2x * 7x)) = 0
(-88 + 16x + (-77x + 14x2)) = 0

Combine like terms: 16x + -77x = -61x
(-88 + -61x + 14x2) = 0

Solving
-88 + -61x + 14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -7x)(11 + -2x) = 0


Subproblem 1
Set the factor '(-8 + -7x)' equal to zero and attempt to solve:

Simplifying
-8 + -7x = 0

Solving
-8 + -7x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7x = 0 + 8
-7x = 0 + 8

Combine like terms: 0 + 8 = 8
-7x = 8

Divide each side by '-7'.
x = -1.142857143

Simplifying
x = -1.142857143

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 = {-1.142857143, 5.5}

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