1-12(x-2)+35(x-2)(x-2)=0

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Solution for 1-12(x-2)+35(x-2)(x-2)=0 equation: 


Simplifying
1 + -12(x + -2) + 35(x + -2)(x + -2) = 0

Reorder the terms:
1 + -12(-2 + x) + 35(x + -2)(x + -2) = 0
1 + (-2 * -12 + x * -12) + 35(x + -2)(x + -2) = 0
1 + (24 + -12x) + 35(x + -2)(x + -2) = 0

Reorder the terms:
1 + 24 + -12x + 35(-2 + x)(x + -2) = 0

Reorder the terms:
1 + 24 + -12x + 35(-2 + x)(-2 + x) = 0

Multiply (-2 + x) * (-2 + x)
1 + 24 + -12x + 35(-2(-2 + x) + x(-2 + x)) = 0
1 + 24 + -12x + 35((-2 * -2 + x * -2) + x(-2 + x)) = 0
1 + 24 + -12x + 35((4 + -2x) + x(-2 + x)) = 0
1 + 24 + -12x + 35(4 + -2x + (-2 * x + x * x)) = 0
1 + 24 + -12x + 35(4 + -2x + (-2x + x2)) = 0

Combine like terms: -2x + -2x = -4x
1 + 24 + -12x + 35(4 + -4x + x2) = 0
1 + 24 + -12x + (4 * 35 + -4x * 35 + x2 * 35) = 0
1 + 24 + -12x + (140 + -140x + 35x2) = 0

Reorder the terms:
1 + 24 + 140 + -12x + -140x + 35x2 = 0

Combine like terms: 1 + 24 = 25
25 + 140 + -12x + -140x + 35x2 = 0

Combine like terms: 25 + 140 = 165
165 + -12x + -140x + 35x2 = 0

Combine like terms: -12x + -140x = -152x
165 + -152x + 35x2 = 0

Solving
165 + -152x + 35x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(15 + -7x)(11 + -5x) = 0


Subproblem 1
Set the factor '(15 + -7x)' equal to zero and attempt to solve:

Simplifying
15 + -7x = 0

Solving
15 + -7x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -7x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -7x = 0 + -15
-7x = 0 + -15

Combine like terms: 0 + -15 = -15
-7x = -15

Divide each side by '-7'.
x = 2.142857143

Simplifying
x = 2.142857143

Subproblem 2
Set the factor '(11 + -5x)' equal to zero and attempt to solve:

Simplifying
11 + -5x = 0

Solving
11 + -5x = 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 + -5x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5x = 0 + -11
-5x = 0 + -11

Combine like terms: 0 + -11 = -11
-5x = -11

Divide each side by '-5'.
x = 2.2

Simplifying
x = 2.2
Solution
x = {2.142857143, 2.2}

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