=(3x+4)(5x-2)

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Solution for =(3x+4)(5x-2) equation: 


Simplifying
0 = (3x + 4)(5x + -2)

Reorder the terms:
0 = (4 + 3x)(5x + -2)

Reorder the terms:
0 = (4 + 3x)(-2 + 5x)

Multiply (4 + 3x) * (-2 + 5x)
0 = (4(-2 + 5x) + 3x * (-2 + 5x))
0 = ((-2 * 4 + 5x * 4) + 3x * (-2 + 5x))
0 = ((-8 + 20x) + 3x * (-2 + 5x))
0 = (-8 + 20x + (-2 * 3x + 5x * 3x))
0 = (-8 + 20x + (-6x + 15x2))

Combine like terms: 20x + -6x = 14x
0 = (-8 + 14x + 15x2)

Solving
0 = -8 + 14x + 15x2

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + -14x + -15x2 = -8 + 14x + 15x2 + 8 + -14x + -15x2

Reorder the terms:
8 + -14x + -15x2 = -8 + 8 + 14x + -14x + 15x2 + -15x2

Combine like terms: -8 + 8 = 0
8 + -14x + -15x2 = 0 + 14x + -14x + 15x2 + -15x2
8 + -14x + -15x2 = 14x + -14x + 15x2 + -15x2

Combine like terms: 14x + -14x = 0
8 + -14x + -15x2 = 0 + 15x2 + -15x2
8 + -14x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
8 + -14x + -15x2 = 0

Factor a trinomial.
(2 + -5x)(4 + 3x) = 0


Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

Subproblem 2
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
Solution
x = {0.4, -1.333333333}

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