=(5x+7)(-3x+2)

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Solution for =(5x+7)(-3x+2) equation: 


Simplifying
0 = (5x + 7)(-3x + 2)

Reorder the terms:
0 = (7 + 5x)(-3x + 2)

Reorder the terms:
0 = (7 + 5x)(2 + -3x)

Multiply (7 + 5x) * (2 + -3x)
0 = (7(2 + -3x) + 5x * (2 + -3x))
0 = ((2 * 7 + -3x * 7) + 5x * (2 + -3x))
0 = ((14 + -21x) + 5x * (2 + -3x))
0 = (14 + -21x + (2 * 5x + -3x * 5x))
0 = (14 + -21x + (10x + -15x2))

Combine like terms: -21x + 10x = -11x
0 = (14 + -11x + -15x2)

Solving
0 = 14 + -11x + -15x2

Solving for variable 'x'.

Combine like terms: 0 + -14 = -14
-14 + 11x + 15x2 = 14 + -11x + -15x2 + -14 + 11x + 15x2

Reorder the terms:
-14 + 11x + 15x2 = 14 + -14 + -11x + 11x + -15x2 + 15x2

Combine like terms: 14 + -14 = 0
-14 + 11x + 15x2 = 0 + -11x + 11x + -15x2 + 15x2
-14 + 11x + 15x2 = -11x + 11x + -15x2 + 15x2

Combine like terms: -11x + 11x = 0
-14 + 11x + 15x2 = 0 + -15x2 + 15x2
-14 + 11x + 15x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
-14 + 11x + 15x2 = 0

Factor a trinomial.
(-7 + -5x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-7 + -5x)' equal to zero and attempt to solve:

Simplifying
-7 + -5x = 0

Solving
-7 + -5x = 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 + -5x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5x = 0 + 7
-5x = 0 + 7

Combine like terms: 0 + 7 = 7
-5x = 7

Divide each side by '-5'.
x = -1.4

Simplifying
x = -1.4

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1.4, 0.6666666667}

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