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

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


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

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

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

Multiply (-7 + x) * (5 + -4x)
(-7(5 + -4x) + x(5 + -4x)) = 0
((5 * -7 + -4x * -7) + x(5 + -4x)) = 0
((-35 + 28x) + x(5 + -4x)) = 0
(-35 + 28x + (5 * x + -4x * x)) = 0
(-35 + 28x + (5x + -4x2)) = 0

Combine like terms: 28x + 5x = 33x
(-35 + 33x + -4x2) = 0

Solving
-35 + 33x + -4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + x)(5 + -4x) = 0


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

Simplifying
-7 + x = 0

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

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

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

Simplifying
x = 7

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {7, 1.25}

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