(x-7)(3x+5)+(x-7)(2x+4)=0

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Solution for (x-7)(3x+5)+(x-7)(2x+4)=0 equation: 


Simplifying
(x + -7)(3x + 5) + (x + -7)(2x + 4) = 0

Reorder the terms:
(-7 + x)(3x + 5) + (x + -7)(2x + 4) = 0

Reorder the terms:
(-7 + x)(5 + 3x) + (x + -7)(2x + 4) = 0

Multiply (-7 + x) * (5 + 3x)
(-7(5 + 3x) + x(5 + 3x)) + (x + -7)(2x + 4) = 0
((5 * -7 + 3x * -7) + x(5 + 3x)) + (x + -7)(2x + 4) = 0
((-35 + -21x) + x(5 + 3x)) + (x + -7)(2x + 4) = 0
(-35 + -21x + (5 * x + 3x * x)) + (x + -7)(2x + 4) = 0
(-35 + -21x + (5x + 3x2)) + (x + -7)(2x + 4) = 0

Combine like terms: -21x + 5x = -16x
(-35 + -16x + 3x2) + (x + -7)(2x + 4) = 0

Reorder the terms:
-35 + -16x + 3x2 + (-7 + x)(2x + 4) = 0

Reorder the terms:
-35 + -16x + 3x2 + (-7 + x)(4 + 2x) = 0

Multiply (-7 + x) * (4 + 2x)
-35 + -16x + 3x2 + (-7(4 + 2x) + x(4 + 2x)) = 0
-35 + -16x + 3x2 + ((4 * -7 + 2x * -7) + x(4 + 2x)) = 0
-35 + -16x + 3x2 + ((-28 + -14x) + x(4 + 2x)) = 0
-35 + -16x + 3x2 + (-28 + -14x + (4 * x + 2x * x)) = 0
-35 + -16x + 3x2 + (-28 + -14x + (4x + 2x2)) = 0

Combine like terms: -14x + 4x = -10x
-35 + -16x + 3x2 + (-28 + -10x + 2x2) = 0

Reorder the terms:
-35 + -28 + -16x + -10x + 3x2 + 2x2 = 0

Combine like terms: -35 + -28 = -63
-63 + -16x + -10x + 3x2 + 2x2 = 0

Combine like terms: -16x + -10x = -26x
-63 + -26x + 3x2 + 2x2 = 0

Combine like terms: 3x2 + 2x2 = 5x2
-63 + -26x + 5x2 = 0

Solving
-63 + -26x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -5x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -5x)' equal to zero and attempt to solve:

Simplifying
-9 + -5x = 0

Solving
-9 + -5x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -5x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5x = 0 + 9
-5x = 0 + 9

Combine like terms: 0 + 9 = 9
-5x = 9

Divide each side by '-5'.
x = -1.8

Simplifying
x = -1.8

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.8, 7}

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