0=4x^2+32x+15

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Solution for 0=4x^2+32x+15 equation:


Simplifying
0 = 4x2 + 32x + 15

Reorder the terms:
0 = 15 + 32x + 4x2

Solving
0 = 15 + 32x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + -32x + -4x2 = 15 + 32x + 4x2 + -15 + -32x + -4x2

Reorder the terms:
-15 + -32x + -4x2 = 15 + -15 + 32x + -32x + 4x2 + -4x2

Combine like terms: 15 + -15 = 0
-15 + -32x + -4x2 = 0 + 32x + -32x + 4x2 + -4x2
-15 + -32x + -4x2 = 32x + -32x + 4x2 + -4x2

Combine like terms: 32x + -32x = 0
-15 + -32x + -4x2 = 0 + 4x2 + -4x2
-15 + -32x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-15 + -32x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 32x + 4x2) = 0

Factor a trinomial.
-1((15 + 2x)(1 + 2x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(15 + 2x)' equal to zero and attempt to solve: Simplifying 15 + 2x = 0 Solving 15 + 2x = 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 + 2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2x = 0 + -15 2x = 0 + -15 Combine like terms: 0 + -15 = -15 2x = -15 Divide each side by '2'. x = -7.5 Simplifying x = -7.5

Subproblem 2

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

Solution

x = {-7.5, -0.5}

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