21x^2+5-35=3x^2-4x

Solution for 21x^2+5-35=3x^2-4x equation:

Simplifying
21x2 + 5 + -35 = 3x2 + -4x

Reorder the terms:
5 + -35 + 21x2 = 3x2 + -4x

Combine like terms: 5 + -35 = -30
-30 + 21x2 = 3x2 + -4x

Reorder the terms:
-30 + 21x2 = -4x + 3x2

Solving
-30 + 21x2 = -4x + 3x2

Solving for variable 'x'.

Reorder the terms:
-30 + 4x + 21x2 + -3x2 = -4x + 3x2 + 4x + -3x2

Combine like terms: 21x2 + -3x2 = 18x2
-30 + 4x + 18x2 = -4x + 3x2 + 4x + -3x2

Reorder the terms:
-30 + 4x + 18x2 = -4x + 4x + 3x2 + -3x2

Combine like terms: -4x + 4x = 0
-30 + 4x + 18x2 = 0 + 3x2 + -3x2
-30 + 4x + 18x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-30 + 4x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 2x + 9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + 2x + 9x2)' equal to zero and attempt to solve:

Simplifying
-15 + 2x + 9x2 = 0

Solving
-15 + 2x + 9x2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-1.666666667 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 0.2222222222x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 0.2222222222x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 0.2222222222x + x2 = 0 + 1.666666667
0.2222222222x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
0.2222222222x + x2 = 1.666666667

The x term is 0.2222222222x.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222x + 0.01234567901 + x2 = 1.666666667 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 1.666666667 + 0.01234567901

Combine like terms: 1.666666667 + 0.01234567901 = 1.67901234601
0.01234567901 + 0.2222222222x + x2 = 1.67901234601

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 1.67901234601

Calculate the square root of the right side: 1.295767088

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 1.295767088 and -1.295767088.

Subproblem 1
x + 0.1111111111 = 1.295767088

Simplifying
x + 0.1111111111 = 1.295767088

Reorder the terms:
0.1111111111 + x = 1.295767088

Solving
0.1111111111 + x = 1.295767088

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = 1.295767088 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = 1.295767088 + -0.1111111111
x = 1.295767088 + -0.1111111111

Combine like terms: 1.295767088 + -0.1111111111 = 1.1846559769
x = 1.1846559769

Simplifying
x = 1.1846559769

Subproblem 2
x + 0.1111111111 = -1.295767088

Simplifying
x + 0.1111111111 = -1.295767088

Reorder the terms:
0.1111111111 + x = -1.295767088

Solving
0.1111111111 + x = -1.295767088

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = -1.295767088 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = -1.295767088 + -0.1111111111
x = -1.295767088 + -0.1111111111

Combine like terms: -1.295767088 + -0.1111111111 = -1.4068781991
x = -1.4068781991

Simplifying
x = -1.4068781991

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1846559769, -1.4068781991}
Solution
x = {1.1846559769, -1.4068781991}