2x^2-13x+19=(x-7)(x-7)

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Solution for 2x^2-13x+19=(x-7)(x-7) equation: 


Simplifying
2x2 + -13x + 19 = (x + -7)(x + -7)

Reorder the terms:
19 + -13x + 2x2 = (x + -7)(x + -7)

Reorder the terms:
19 + -13x + 2x2 = (-7 + x)(x + -7)

Reorder the terms:
19 + -13x + 2x2 = (-7 + x)(-7 + x)

Multiply (-7 + x) * (-7 + x)
19 + -13x + 2x2 = (-7(-7 + x) + x(-7 + x))
19 + -13x + 2x2 = ((-7 * -7 + x * -7) + x(-7 + x))
19 + -13x + 2x2 = ((49 + -7x) + x(-7 + x))
19 + -13x + 2x2 = (49 + -7x + (-7 * x + x * x))
19 + -13x + 2x2 = (49 + -7x + (-7x + x2))

Combine like terms: -7x + -7x = -14x
19 + -13x + 2x2 = (49 + -14x + x2)

Solving
19 + -13x + 2x2 = 49 + -14x + x2

Solving for variable 'x'.

Reorder the terms:
19 + -49 + -13x + 14x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 19 + -49 = -30
-30 + -13x + 14x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: -13x + 14x = 1x
-30 + 1x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-30 + 1x + 1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Reorder the terms:
-30 + 1x + 1x2 = 49 + -49 + -14x + 14x + x2 + -1x2

Combine like terms: 49 + -49 = 0
-30 + 1x + 1x2 = 0 + -14x + 14x + x2 + -1x2
-30 + 1x + 1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
-30 + 1x + 1x2 = 0 + x2 + -1x2
-30 + 1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-30 + 1x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -1x) = 0


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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}

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