0=8x^2+30x+7

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Solution for 0=8x^2+30x+7 equation: 


Simplifying
0 = 8x2 + 30x + 7

Reorder the terms:
0 = 7 + 30x + 8x2

Solving
0 = 7 + 30x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -7 = -7
-7 + -30x + -8x2 = 7 + 30x + 8x2 + -7 + -30x + -8x2

Reorder the terms:
-7 + -30x + -8x2 = 7 + -7 + 30x + -30x + 8x2 + -8x2

Combine like terms: 7 + -7 = 0
-7 + -30x + -8x2 = 0 + 30x + -30x + 8x2 + -8x2
-7 + -30x + -8x2 = 30x + -30x + 8x2 + -8x2

Combine like terms: 30x + -30x = 0
-7 + -30x + -8x2 = 0 + 8x2 + -8x2
-7 + -30x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-7 + -30x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 30x + 8x2) = 0

Factor a trinomial.
-1((7 + 2x)(1 + 4x)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-3.5, -0.25}

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