0=4x^2+24x-13

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Solution for 0=4x^2+24x-13 equation: 


Simplifying
0 = 4x2 + 24x + -13

Reorder the terms:
0 = -13 + 24x + 4x2

Solving
0 = -13 + 24x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 13 = 13
13 + -24x + -4x2 = -13 + 24x + 4x2 + 13 + -24x + -4x2

Reorder the terms:
13 + -24x + -4x2 = -13 + 13 + 24x + -24x + 4x2 + -4x2

Combine like terms: -13 + 13 = 0
13 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2
13 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2

Combine like terms: 24x + -24x = 0
13 + -24x + -4x2 = 0 + 4x2 + -4x2
13 + -24x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
13 + -24x + -4x2 = 0

Factor a trinomial.
(1 + -2x)(13 + 2x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(13 + 2x)' equal to zero and attempt to solve:

Simplifying
13 + 2x = 0

Solving
13 + 2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13

Combine like terms: 0 + -13 = -13
2x = -13

Divide each side by '2'.
x = -6.5

Simplifying
x = -6.5
Solution
x = {0.5, -6.5}

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