4x(x+3)=2(x+7)

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Solution for 4x(x+3)=2(x+7) equation: 


Simplifying
4x(x + 3) = 2(x + 7)

Reorder the terms:
4x(3 + x) = 2(x + 7)
(3 * 4x + x * 4x) = 2(x + 7)
(12x + 4x2) = 2(x + 7)

Reorder the terms:
12x + 4x2 = 2(7 + x)
12x + 4x2 = (7 * 2 + x * 2)
12x + 4x2 = (14 + 2x)

Solving
12x + 4x2 = 14 + 2x

Solving for variable 'x'.

Reorder the terms:
-14 + 12x + -2x + 4x2 = 14 + 2x + -14 + -2x

Combine like terms: 12x + -2x = 10x
-14 + 10x + 4x2 = 14 + 2x + -14 + -2x

Reorder the terms:
-14 + 10x + 4x2 = 14 + -14 + 2x + -2x

Combine like terms: 14 + -14 = 0
-14 + 10x + 4x2 = 0 + 2x + -2x
-14 + 10x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-14 + 10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 5x + 2x2) = 0

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

Ignore the factor 2.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-3.5, 1}

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