3x^2+34x+10=-5x^2+68x-11

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Solution for 3x^2+34x+10=-5x^2+68x-11 equation: 


Simplifying
3x2 + 34x + 10 = -5x2 + 68x + -11

Reorder the terms:
10 + 34x + 3x2 = -5x2 + 68x + -11

Reorder the terms:
10 + 34x + 3x2 = -11 + 68x + -5x2

Solving
10 + 34x + 3x2 = -11 + 68x + -5x2

Solving for variable 'x'.

Reorder the terms:
10 + 11 + 34x + -68x + 3x2 + 5x2 = -11 + 68x + -5x2 + 11 + -68x + 5x2

Combine like terms: 10 + 11 = 21
21 + 34x + -68x + 3x2 + 5x2 = -11 + 68x + -5x2 + 11 + -68x + 5x2

Combine like terms: 34x + -68x = -34x
21 + -34x + 3x2 + 5x2 = -11 + 68x + -5x2 + 11 + -68x + 5x2

Combine like terms: 3x2 + 5x2 = 8x2
21 + -34x + 8x2 = -11 + 68x + -5x2 + 11 + -68x + 5x2

Reorder the terms:
21 + -34x + 8x2 = -11 + 11 + 68x + -68x + -5x2 + 5x2

Combine like terms: -11 + 11 = 0
21 + -34x + 8x2 = 0 + 68x + -68x + -5x2 + 5x2
21 + -34x + 8x2 = 68x + -68x + -5x2 + 5x2

Combine like terms: 68x + -68x = 0
21 + -34x + 8x2 = 0 + -5x2 + 5x2
21 + -34x + 8x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
21 + -34x + 8x2 = 0

Factor a trinomial.
(3 + -4x)(7 + -2x) = 0


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0.75, 3.5}

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