x(2x-5)-7=11

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Solution for x(2x-5)-7=11 equation: 


Simplifying
x(2x + -5) + -7 = 11

Reorder the terms:
x(-5 + 2x) + -7 = 11
(-5 * x + 2x * x) + -7 = 11
(-5x + 2x2) + -7 = 11

Reorder the terms:
-7 + -5x + 2x2 = 11

Solving
-7 + -5x + 2x2 = 11

Solving for variable 'x'.

Reorder the terms:
-7 + -11 + -5x + 2x2 = 11 + -11

Combine like terms: -7 + -11 = -18
-18 + -5x + 2x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-18 + -5x + 2x2 = 0

Factor a trinomial.
(-2 + -1x)(9 + -2x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-2, 4.5}

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