=((6x+7)(12x+5))

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Solution for =((6x+7)(12x+5)) equation:


Simplifying
0 = ((6x + 7)(12x + 5))

Reorder the terms:
0 = ((7 + 6x)(12x + 5))

Reorder the terms:
0 = ((7 + 6x)(5 + 12x))

Multiply (7 + 6x) * (5 + 12x)
0 = ((7(5 + 12x) + 6x * (5 + 12x)))
0 = (((5 * 7 + 12x * 7) + 6x * (5 + 12x)))
0 = (((35 + 84x) + 6x * (5 + 12x)))
0 = ((35 + 84x + (5 * 6x + 12x * 6x)))
0 = ((35 + 84x + (30x + 72x2)))

Combine like terms: 84x + 30x = 114x
0 = ((35 + 114x + 72x2))
0 = (35 + 114x + 72x2)

Remove parenthesis around (35 + 114x + 72x2)
0 = 35 + 114x + 72x2

Solving
0 = 35 + 114x + 72x2

Solving for variable 'x'.

Combine like terms: 0 + -35 = -35
-35 + -114x + -72x2 = 35 + 114x + 72x2 + -35 + -114x + -72x2

Reorder the terms:
-35 + -114x + -72x2 = 35 + -35 + 114x + -114x + 72x2 + -72x2

Combine like terms: 35 + -35 = 0
-35 + -114x + -72x2 = 0 + 114x + -114x + 72x2 + -72x2
-35 + -114x + -72x2 = 114x + -114x + 72x2 + -72x2

Combine like terms: 114x + -114x = 0
-35 + -114x + -72x2 = 0 + 72x2 + -72x2
-35 + -114x + -72x2 = 72x2 + -72x2

Combine like terms: 72x2 + -72x2 = 0
-35 + -114x + -72x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 114x + 72x2) = 0

Factor a trinomial.
-1((7 + 6x)(5 + 12x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(7 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 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 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Divide each side by '6'. x = -1.166666667 Simplifying x = -1.166666667

Subproblem 2

Set the factor '(5 + 12x)' equal to zero and attempt to solve: Simplifying 5 + 12x = 0 Solving 5 + 12x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 12x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 12x = 0 + -5 12x = 0 + -5 Combine like terms: 0 + -5 = -5 12x = -5 Divide each side by '12'. x = -0.4166666667 Simplifying x = -0.4166666667

Solution

x = {-1.166666667, -0.4166666667}

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