36x^2+48x+16=7(-6x-4)-12

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Solution for 36x^2+48x+16=7(-6x-4)-12 equation:


Simplifying
36x2 + 48x + 16 = 7(-6x + -4) + -12

Reorder the terms:
16 + 48x + 36x2 = 7(-6x + -4) + -12

Reorder the terms:
16 + 48x + 36x2 = 7(-4 + -6x) + -12
16 + 48x + 36x2 = (-4 * 7 + -6x * 7) + -12
16 + 48x + 36x2 = (-28 + -42x) + -12

Reorder the terms:
16 + 48x + 36x2 = -28 + -12 + -42x

Combine like terms: -28 + -12 = -40
16 + 48x + 36x2 = -40 + -42x

Solving
16 + 48x + 36x2 = -40 + -42x

Solving for variable 'x'.

Reorder the terms:
16 + 40 + 48x + 42x + 36x2 = -40 + -42x + 40 + 42x

Combine like terms: 16 + 40 = 56
56 + 48x + 42x + 36x2 = -40 + -42x + 40 + 42x

Combine like terms: 48x + 42x = 90x
56 + 90x + 36x2 = -40 + -42x + 40 + 42x

Reorder the terms:
56 + 90x + 36x2 = -40 + 40 + -42x + 42x

Combine like terms: -40 + 40 = 0
56 + 90x + 36x2 = 0 + -42x + 42x
56 + 90x + 36x2 = -42x + 42x

Combine like terms: -42x + 42x = 0
56 + 90x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + 45x + 18x2) = 0

Factor a trinomial.
2((4 + 3x)(7 + 6x)) = 0

Ignore the factor 2.

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

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

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

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

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

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
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
Solution
x = {-1.333333333, -1.166666667}

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