7x(2x+2)=12(5x-1)

Solution for 7x(2x+2)=12(5x-1) equation:

Simplifying
7x(2x + 2) = 12(5x + -1)

Reorder the terms:
7x(2 + 2x) = 12(5x + -1)
(2 * 7x + 2x * 7x) = 12(5x + -1)
(14x + 14x2) = 12(5x + -1)

Reorder the terms:
14x + 14x2 = 12(-1 + 5x)
14x + 14x2 = (-1 * 12 + 5x * 12)
14x + 14x2 = (-12 + 60x)

Solving
14x + 14x2 = -12 + 60x

Solving for variable 'x'.

Reorder the terms:
12 + 14x + -60x + 14x2 = -12 + 60x + 12 + -60x

Combine like terms: 14x + -60x = -46x
12 + -46x + 14x2 = -12 + 60x + 12 + -60x

Reorder the terms:
12 + -46x + 14x2 = -12 + 12 + 60x + -60x

Combine like terms: -12 + 12 = 0
12 + -46x + 14x2 = 0 + 60x + -60x
12 + -46x + 14x2 = 60x + -60x

Combine like terms: 60x + -60x = 0
12 + -46x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -23x + 7x2) = 0

Factor a trinomial.
2((2 + -7x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.2857142857, 3}